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All questions of Coordinate Geometry for Class 9 Exam
The point (–2, –3) belongs to Quadrant :- a)Q1
- b)Q2
- c)Q3
- d)Q4
Correct answer is option 'C'. Can you explain this answer?
The point (–2, –3) belongs to Quadrant :
a)
Q1
b)
Q2
c)
Q3
d)
Q4
|
Zachary Foster answered |
The point (-2, -3) is located in the third quadrant. This is because both the x coordinate and the y coordinate are negative, which are the characteristics of points in Quadrant III.
The correct answer is: C: Q3
The correct answer is: C: Q3
A point of the form (0, b) lies on
- a)x- axis
- b)quadrant III
- c)quadrant I
- d)y- axis
Correct answer is option 'D'. Can you explain this answer?
A point of the form (0, b) lies on
a)
x- axis
b)
quadrant III
c)
quadrant I
d)
y- axis
|
Rati Joshi answered |
Explanation:
The point (0, b) is a point in the coordinate plane, where the first coordinate (x-coordinate) is 0, and the second coordinate (y-coordinate) is b.
To determine on which axis or quadrant this point lies, we need to examine the values of the coordinates:
- The x-coordinate is 0, which means the point lies on the y-axis.
- The y-coordinate is b, which means the point is at a distance of b units from the origin, in the positive y-direction (since b is positive).
Therefore, the point (0, b) lies on the y-axis.
Option D, which says "y-axis", is the correct answer.
The point (0, b) is a point in the coordinate plane, where the first coordinate (x-coordinate) is 0, and the second coordinate (y-coordinate) is b.
To determine on which axis or quadrant this point lies, we need to examine the values of the coordinates:
- The x-coordinate is 0, which means the point lies on the y-axis.
- The y-coordinate is b, which means the point is at a distance of b units from the origin, in the positive y-direction (since b is positive).
Therefore, the point (0, b) lies on the y-axis.
Option D, which says "y-axis", is the correct answer.
The point (–3, 2) belongs to Quadrant _______________ :- a)Q1
- b)Q2
- c)Q3
- d)Q4
Correct answer is option 'B'. Can you explain this answer?
The point (–3, 2) belongs to Quadrant _______________ :
a)
Q1
b)
Q2
c)
Q3
d)
Q4
|
Tanvi Shah answered |
Sorry, but I can't generate a response without more information. Could you please provide the missing details?
If the abscissa of a point is y and the ordinate is x then the coordinates of the point are ……..
- a)(x, 0)
- b)(y, x)
- c)(x, y)
- d)(0, y)
Correct answer is option 'B'. Can you explain this answer?
If the abscissa of a point is y and the ordinate is x then the coordinates of the point are ……..
a)
(x, 0)
b)
(y, x)
c)
(x, y)
d)
(0, y)
|
|
Zachary Foster answered |
The correct answer is B: (y, x).
- The abscissa of a point is the x-coordinate.
- The ordinate of a point is the y-coordinate.
- Therefore, if the abscissa of a point is y and the ordinate is x, the coordinates of the point will be (y, x).
- The abscissa of a point is the x-coordinate.
- The ordinate of a point is the y-coordinate.
- Therefore, if the abscissa of a point is y and the ordinate is x, the coordinates of the point will be (y, x).
The point A(3, 4) lies in
- a)II Quadrant
- b)I Quadrant
- c)IV Quadrant
- d)III Quadrant
Correct answer is option 'B'. Can you explain this answer?
The point A(3, 4) lies in
a)
II Quadrant
b)
I Quadrant
c)
IV Quadrant
d)
III Quadrant
|
|
Aradhiya Gupta answered |
A(3, 4) are found in I quadrant because both the cordinates are positive
If x = y then (x, y) = (y, x)- a)The above statement is TRUE
- b)The above statement is TRUE if x < y
- c)The above statement is FALSE
- d)The above statement is TRUE if x ≠ y
Correct answer is option 'A'. Can you explain this answer?
If x = y then (x, y) = (y, x)
a)
The above statement is TRUE
b)
The above statement is TRUE if x < y
c)
The above statement is FALSE
d)
The above statement is TRUE if x ≠ y
|
Palak Mukherjee answered |
Explanation:
The statement "If x = y then (x, y) = (y, x)" is a mathematical statement that involves the relationship between two variables, x and y. Let's break down the statement and see why option A is the correct answer.
If x = y:
If x and y are equal, then we can substitute y for x or x for y in any equation involving x and y.
(x, y) = (y, x):
This statement means that the ordered pair (x, y) is equal to the ordered pair (y, x). In other words, the order of the values in the ordered pair does not matter.
Therefore, if x = y, then (x, y) = (y, x). This is because the values in the ordered pair are the same, regardless of which value is listed first.
For example, if x = 3 and y = 3, then (x, y) = (3, 3) and (y, x) = (3, 3). Both ordered pairs are equal, so the statement is true.
Conclusion:
Therefore, option A is the correct answer because the statement "If x = y then (x, y) = (y, x)" is true regardless of the values of x and y as long as x and y are equal.
The statement "If x = y then (x, y) = (y, x)" is a mathematical statement that involves the relationship between two variables, x and y. Let's break down the statement and see why option A is the correct answer.
If x = y:
If x and y are equal, then we can substitute y for x or x for y in any equation involving x and y.
(x, y) = (y, x):
This statement means that the ordered pair (x, y) is equal to the ordered pair (y, x). In other words, the order of the values in the ordered pair does not matter.
Therefore, if x = y, then (x, y) = (y, x). This is because the values in the ordered pair are the same, regardless of which value is listed first.
For example, if x = 3 and y = 3, then (x, y) = (3, 3) and (y, x) = (3, 3). Both ordered pairs are equal, so the statement is true.
Conclusion:
Therefore, option A is the correct answer because the statement "If x = y then (x, y) = (y, x)" is true regardless of the values of x and y as long as x and y are equal.
The abscissa or x-coordinate of any point on Y-axis is:
- a)Three
- b)Two
- c)One
- d)Zero
Correct answer is option 'D'. Can you explain this answer?
The abscissa or x-coordinate of any point on Y-axis is:
a)
Three
b)
Two
c)
One
d)
Zero
|
|
Anirudh Singh answered |
Explanation:
The Y-axis is the vertical line on a Cartesian plane. It is perpendicular to the X-axis, which is the horizontal line on the same plane. Any point on the Y-axis has an x-coordinate of zero because it lies directly on the Y-axis, which is a line passing through the origin of the plane. Here are some more details:
• Definition of abscissa: The abscissa is the x-coordinate of a point on a Cartesian plane. It is measured from the vertical Y-axis to the point in question.
• Understanding the Y-axis: The Y-axis is a vertical line that runs through the origin of the plane. It consists of all points with an x-coordinate of zero.
• Relationship between the X and Y axes: The X and Y axes intersect at the origin of the plane, which has coordinates (0,0). Any point on the X-axis has a y-coordinate of zero, and any point on the Y-axis has an x-coordinate of zero.
• Importance of the origin: The origin of the plane is the starting point for measuring coordinates. It is where the X and Y axes intersect, and it has coordinates (0,0). All other points on the plane can be located relative to the origin.
• Conclusion: The abscissa or x-coordinate of any point on the Y-axis is zero because the Y-axis consists of all points with an x-coordinate of zero.
The Y-axis is the vertical line on a Cartesian plane. It is perpendicular to the X-axis, which is the horizontal line on the same plane. Any point on the Y-axis has an x-coordinate of zero because it lies directly on the Y-axis, which is a line passing through the origin of the plane. Here are some more details:
• Definition of abscissa: The abscissa is the x-coordinate of a point on a Cartesian plane. It is measured from the vertical Y-axis to the point in question.
• Understanding the Y-axis: The Y-axis is a vertical line that runs through the origin of the plane. It consists of all points with an x-coordinate of zero.
• Relationship between the X and Y axes: The X and Y axes intersect at the origin of the plane, which has coordinates (0,0). Any point on the X-axis has a y-coordinate of zero, and any point on the Y-axis has an x-coordinate of zero.
• Importance of the origin: The origin of the plane is the starting point for measuring coordinates. It is where the X and Y axes intersect, and it has coordinates (0,0). All other points on the plane can be located relative to the origin.
• Conclusion: The abscissa or x-coordinate of any point on the Y-axis is zero because the Y-axis consists of all points with an x-coordinate of zero.
For a line whose equation is 2x + y = 5, which one of the following points lies on it ?- a)(3, 2)
- b)(1, 2)
- c)(2, 1)
- d)(-2, 1)
Correct answer is 'C'. Can you explain this answer?
For a line whose equation is 2x + y = 5, which one of the following points lies on it ?
a)
(3, 2)
b)
(1, 2)
c)
(2, 1)
d)
(-2, 1)
|
Kanayalal Parchwani answered |
Suppose x value is 2 and y value is 1 so 2(2)+1=5
The point (3, 2) belongs to quadrant _______________ :- a)Q1
- b)Q2
- c)Q3
- d)Q4
Correct answer is option 'A'. Can you explain this answer?
The point (3, 2) belongs to quadrant _______________ :
a)
Q1
b)
Q2
c)
Q3
d)
Q4
|
|
Isha Nair answered |
Explanation:
Quadrants are the four regions in a coordinate plane which are separated by the x-axis and y-axis. These quadrants are numbered from 1 to 4 in a counterclockwise direction. Let's understand how to identify the quadrant in which a point lies:
- Quadrant 1 (Q1): This quadrant is on the right side of the y-axis and above the x-axis. The values of x and y are both positive in this quadrant. So, any point lying in this quadrant has positive values for both x and y coordinates.
- Quadrant 2 (Q2): This quadrant is on the left side of the y-axis and above the x-axis. The value of x is negative and the value of y is positive in this quadrant. So, any point lying in this quadrant has negative x-coordinate and positive y-coordinate.
- Quadrant 3 (Q3): This quadrant is on the left side of the y-axis and below the x-axis. The values of both x and y are negative in this quadrant. So, any point lying in this quadrant has negative values for both x and y coordinates.
- Quadrant 4 (Q4): This quadrant is on the right side of the y-axis and below the x-axis. The value of x is positive and the value of y is negative in this quadrant. So, any point lying in this quadrant has positive x-coordinate and negative y-coordinate.
Now, let's identify in which quadrant the point (3, 2) lies:
- The x-coordinate of the point is 3 which is positive.
- The y-coordinate of the point is 2 which is also positive.
Since both the x and y-coordinates of the point are positive, it lies in the Quadrant 1 (Q1).
Therefore, the correct answer is option 'A' which says that the point (3, 2) belongs to quadrant Q1.
Quadrants are the four regions in a coordinate plane which are separated by the x-axis and y-axis. These quadrants are numbered from 1 to 4 in a counterclockwise direction. Let's understand how to identify the quadrant in which a point lies:
- Quadrant 1 (Q1): This quadrant is on the right side of the y-axis and above the x-axis. The values of x and y are both positive in this quadrant. So, any point lying in this quadrant has positive values for both x and y coordinates.
- Quadrant 2 (Q2): This quadrant is on the left side of the y-axis and above the x-axis. The value of x is negative and the value of y is positive in this quadrant. So, any point lying in this quadrant has negative x-coordinate and positive y-coordinate.
- Quadrant 3 (Q3): This quadrant is on the left side of the y-axis and below the x-axis. The values of both x and y are negative in this quadrant. So, any point lying in this quadrant has negative values for both x and y coordinates.
- Quadrant 4 (Q4): This quadrant is on the right side of the y-axis and below the x-axis. The value of x is positive and the value of y is negative in this quadrant. So, any point lying in this quadrant has positive x-coordinate and negative y-coordinate.
Now, let's identify in which quadrant the point (3, 2) lies:
- The x-coordinate of the point is 3 which is positive.
- The y-coordinate of the point is 2 which is also positive.
Since both the x and y-coordinates of the point are positive, it lies in the Quadrant 1 (Q1).
Therefore, the correct answer is option 'A' which says that the point (3, 2) belongs to quadrant Q1.
Abscissa of all points on the y-axis is- a)1
- b)any number
- c)0
- d)-1
Correct answer is option 'C'. Can you explain this answer?
Abscissa of all points on the y-axis is
a)
1
b)
any number
c)
0
d)
-1
|
|
Sofiya Khan answered |
Yes, because when abscissa or coordinate of x - axis is 0 the point lies on y - axis.
therefore, the correct answer is option c.
therefore, the correct answer is option c.
Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).
- a)(2, 3)
- b)(11, 2)
- c)(0, 3)
- d)(1, 3)
Correct answer is option 'B'. Can you explain this answer?
Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).
a)
(2, 3)
b)
(11, 2)
c)
(0, 3)
d)
(1, 3)
|
Jyoti Kapoor answered |
The given three points are A(1,2) B(3,-4) and C(5,-6).
Let P (x, y) be the point equidistant from these three points.
So, PA = PB = PC
⇒ x^2 + 1– 2x + y^2 + 4 – 4y = x^2 + 9 -6x + y^2 + 16 + 8y = x 2 + 25– 10x + y^2 + 36 + 12y
⇒ – 2x– 4y + 5 = -6x + 8y +25= – 10x + 12y+61
– 2x– 4y + 5 = -6x + 8y +25
⇒ – 2x– 4y + 5 +6x - 8y -25=0
⇒ 4x– 12y -20=0
⇒ x– 3y - 5 =0....(i)
- 2x– 4y + 5 = – 10x + 12y+61
⇒- 2x– 4y + 5 +10x - 12y-61=0
⇒8x– 16y -56=0
⇒x– 2y -7=0....(ii)
Solving (i) and (ii)
x = 11, y = 2
Thus, the required point is (11, 2)
The coordinate of a point on the y- axis of the form are …….- a)(0, 0)
- b)(x, y)
- c)(0, y)
- d)(x, 0)
Correct answer is option 'C'. Can you explain this answer?
The coordinate of a point on the y- axis of the form are …….
a)
(0, 0)
b)
(x, y)
c)
(0, y)
d)
(x, 0)
|
Shubhangi Rai answered |
This is because absicca should 0 to be on y axis if not it wont be on the axis it would be on the graph somewhere
The point whose abscissa is -3 and lies on x-axis is.
- a)(0,3)
- b)(3,0)
- c)(0,-3)
- d)(-3,0)
Correct answer is option 'D'. Can you explain this answer?
The point whose abscissa is -3 and lies on x-axis is.
a)
(0,3)
b)
(3,0)
c)
(0,-3)
d)
(-3,0)
|
|
Zachary Foster answered |
The abscissa refers to the x-coordinate of a point. If a point lies on the x-axis, its y-coordinate (ordinate) will be zero.
Given that the abscissa is -3 and the point lies on the x-axis, the coordinates of the point will be:
(-3, 0).
Thus, the point is (-3, 0).
The point (0, –2) lies on :- a)+ve x-axis
- b)+ve y-axis
- c)–ve x-axis
- d)–ve y-axis
Correct answer is 'D'. Can you explain this answer?
The point (0, –2) lies on :
a)
+ve x-axis
b)
+ve y-axis
c)
–ve x-axis
d)
–ve y-axis
|
Tarun Bhaskar answered |
Because the other name of Y is X=0 and y=-2so it lies on negative Y axis(-ve Y-axis)
The point (0, -4) lies- a)in quadrant IV
- b)on the negative direction of x-axis
- c)on the negative direction of y-axis
- d)in quadrant III
Correct answer is option 'C'. Can you explain this answer?
The point (0, -4) lies
a)
in quadrant IV
b)
on the negative direction of x-axis
c)
on the negative direction of y-axis
d)
in quadrant III
|
|
Zachary Foster answered |
- The Cartesian coordinate system is divided into four quadrants:
- Quadrant I: Positive x and y values.
- Quadrant II: Negative x, positive y values.
- Quadrant III: Negative x and y values.
- Quadrant IV: Positive x, negative y values.
- The point (0, -4) is on the y-axis, where x = 0.
- This point lies in Quadrant IV.
- Quadrant I: Positive x and y values.
- Quadrant II: Negative x, positive y values.
- Quadrant III: Negative x and y values.
- Quadrant IV: Positive x, negative y values.
- The point (0, -4) is on the y-axis, where x = 0.
- This point lies in Quadrant IV.
The point (2, –3) belongs to quadrant _______________ :- a)Q1
- b)Q2
- c)Q3
- d)Q4
Correct answer is option 'D'. Can you explain this answer?
The point (2, –3) belongs to quadrant _______________ :
a)
Q1
b)
Q2
c)
Q3
d)
Q4
|
Vikram Khanna answered |
The 4th quadrant.
To the right and below the origin.
Explanation:
The x value is POSITIVE which means that the point is to the right of the origin.
The y value is NEGATIVE which means that the point is below the origin.
The 4th quadrant is to the right and below the origin,(The bottom right quadrant)
All points in the 4th quadrant have the signs as (+,−)
The point which lies on y-axis at a distance of 6 units in the positive direction of y-axis is- a)(-6, 0)
- b)(0, -6)
- c)(0, 6)
- d)(6, 0)
Correct answer is option 'C'. Can you explain this answer?
The point which lies on y-axis at a distance of 6 units in the positive direction of y-axis is
a)
(-6, 0)
b)
(0, -6)
c)
(0, 6)
d)
(6, 0)
|
Sakshi Banerjee answered |
Finding the point on y-axis at a distance of 6 units in the positive direction of y-axis
Steps:
1. The point on y-axis is denoted as (0, y), where y is the y-coordinate of the point.
2. Since we want the point to be in the positive direction of y-axis, y should be positive.
3. The distance of the point from the origin is given as 6 units. Using the distance formula, we have:
- distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
- Here, x1 = 0, y1 = 0 (origin), x2 = 0 (point lies on y-axis), y2 = y
- distance = sqrt((0 - 0)^2 + (y - 0)^2) = sqrt(y^2) = y
- Therefore, y = 6
4. So, the point on y-axis at a distance of 6 units in the positive direction of y-axis is (0, 6).
Answer:
The correct answer is option C) (0, 6).
Steps:
1. The point on y-axis is denoted as (0, y), where y is the y-coordinate of the point.
2. Since we want the point to be in the positive direction of y-axis, y should be positive.
3. The distance of the point from the origin is given as 6 units. Using the distance formula, we have:
- distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
- Here, x1 = 0, y1 = 0 (origin), x2 = 0 (point lies on y-axis), y2 = y
- distance = sqrt((0 - 0)^2 + (y - 0)^2) = sqrt(y^2) = y
- Therefore, y = 6
4. So, the point on y-axis at a distance of 6 units in the positive direction of y-axis is (0, 6).
Answer:
The correct answer is option C) (0, 6).
If (2, 2p + 2) is the mid-point of (3p, 4) and (-2, 2q), then the value of p and q are- a)3, 6
- b)7, 9
- c)2, 4
- d)8, 10
Correct answer is option 'C'. Can you explain this answer?
If (2, 2p + 2) is the mid-point of (3p, 4) and (-2, 2q), then the value of p and q are
a)
3, 6
b)
7, 9
c)
2, 4
d)
8, 10
|
Hansa Sharma answered |
we have,
2 = (3p - 2)/2 and 2p + 2 = (2q + 4)/2
3p = 6 and 2p = q
p = 2
and q = 2p = 4
A point both of whose co-ordinates are negative lies in- a)quadrant II and IV
- b)quadrant I and III
- c)quadrant III only
- d)quadrant I only
Correct answer is option 'C'. Can you explain this answer?
A point both of whose co-ordinates are negative lies in
a)
quadrant II and IV
b)
quadrant I and III
c)
quadrant III only
d)
quadrant I only
|
|
Anya answered |
It is because the quadrant 3 has both of the x and y as negative numbers
The point D(3, -6) lies in
- a)II Quadrant
- b)III Quadrant
- c)IV Quadrant
- d)I Quadrant
Correct answer is option 'C'. Can you explain this answer?
The point D(3, -6) lies in
a)
II Quadrant
b)
III Quadrant
c)
IV Quadrant
d)
I Quadrant
|
Keshav answered |
The point D(3, -6) lies in the IV Quadrant. Explanation: In the Cartesian plane, the X-axis and Y-axis divide the plane into four quadrants. The I Quadrant is where both x and y are positive. The II Quadrant is where x is negative and y is positive. The III Quadrant is where both x and y are negative. The IV Quadrant is where x is positive and y is negative. The point D(3, -6) has a positive x-coordinate and a negative y-coordinate. Therefore, it lies in the IV Quadrant.
Which of the following statement is TRUE ?- a)Coordinate (-2, 3) lies in III quadrant whereas (3, -2) lies in the IV quadrant.
- b)Coordinate (-2, 3) lies in II quadrant whereas (3, -2) lies in the III quadrant
- c)Coordinate (-2, 3) and (3, -2) lies in the same quadrant.
- d)Coordinate (-2, 3) lies in II quadrant whereas (3, -2) lies in the IV quadrant.
Correct answer is option 'D'. Can you explain this answer?
Which of the following statement is TRUE ?
a)
Coordinate (-2, 3) lies in III quadrant whereas (3, -2) lies in the IV quadrant.
b)
Coordinate (-2, 3) lies in II quadrant whereas (3, -2) lies in the III quadrant
c)
Coordinate (-2, 3) and (3, -2) lies in the same quadrant.
d)
Coordinate (-2, 3) lies in II quadrant whereas (3, -2) lies in the IV quadrant.
|
Saikat Verma answered |
**Explanation:**
To determine the quadrant in which a coordinate point lies, we need to consider the signs of its x and y coordinates.
Let's analyze the given coordinates:
- Coordinate (-2, 3): The x-coordinate is -2 (negative) and the y-coordinate is 3 (positive).
- Coordinate (3, -2): The x-coordinate is 3 (positive) and the y-coordinate is -2 (negative).
Based on these coordinates, we can determine the quadrants as follows:
- Coordinate (-2, 3): Since the x-coordinate is negative and the y-coordinate is positive, this point lies in the **II quadrant**.
- Coordinate (3, -2): Since the x-coordinate is positive and the y-coordinate is negative, this point lies in the **IV quadrant**.
Therefore, the correct statement is option **D: Coordinate (-2, 3) lies in II quadrant whereas (3, -2) lies in IV quadrant**.
To determine the quadrant in which a coordinate point lies, we need to consider the signs of its x and y coordinates.
Let's analyze the given coordinates:
- Coordinate (-2, 3): The x-coordinate is -2 (negative) and the y-coordinate is 3 (positive).
- Coordinate (3, -2): The x-coordinate is 3 (positive) and the y-coordinate is -2 (negative).
Based on these coordinates, we can determine the quadrants as follows:
- Coordinate (-2, 3): Since the x-coordinate is negative and the y-coordinate is positive, this point lies in the **II quadrant**.
- Coordinate (3, -2): Since the x-coordinate is positive and the y-coordinate is negative, this point lies in the **IV quadrant**.
Therefore, the correct statement is option **D: Coordinate (-2, 3) lies in II quadrant whereas (3, -2) lies in IV quadrant**.
The point (7, 0) lies
- a)in quadrant IV
- b)on the positive direction of y-axis
- c)in quadrant II
- d)on the positive direction of x-axis
Correct answer is option 'D'. Can you explain this answer?
The point (7, 0) lies
a)
in quadrant IV
b)
on the positive direction of y-axis
c)
in quadrant II
d)
on the positive direction of x-axis
|
|
Harini Shah answered |
As it is clear that (7,0) lies in the 1st quadrant it is understood that the positive direction of x-axis is the 1st quadrant. Hence, the answer
The point (0, 9) lies- a)in quadrant IV
- b)on the positive direction of y-axis
- c)in quadrant III
- d)on the positive direction of x-axis
Correct answer is option 'B'. Can you explain this answer?
The point (0, 9) lies
a)
in quadrant IV
b)
on the positive direction of y-axis
c)
in quadrant III
d)
on the positive direction of x-axis
|
Ridhi Kapoor answered |
**Explanation:**
The point (0, 9) lies on the positive direction of the y-axis. Let's break down the options and analyze them one by one to understand why the correct answer is option 'B'.
a) In quadrant IV:
Quadrant IV is the bottom right quadrant on the coordinate plane. In this quadrant, both the x and y coordinates are positive. However, since the x-coordinate of the given point is 0, it does not lie in quadrant IV.
b) On the positive direction of y-axis:
The positive direction of the y-axis is the upward direction. Since the y-coordinate of the given point is 9, which is positive, it lies on the positive direction of the y-axis. Therefore, option 'B' is correct.
c) In quadrant III:
Quadrant III is the bottom left quadrant on the coordinate plane. In this quadrant, the x-coordinate is negative, but the y-coordinate is positive. Since the x-coordinate of the given point is 0, it does not lie in quadrant III.
d) On the positive direction of x-axis:
The positive direction of the x-axis is the rightward direction. However, since the x-coordinate of the given point is 0, it does not lie on the positive direction of the x-axis.
Therefore, the correct answer is option 'B' because the point (0, 9) lies on the positive direction of the y-axis.
The point (0, 9) lies on the positive direction of the y-axis. Let's break down the options and analyze them one by one to understand why the correct answer is option 'B'.
a) In quadrant IV:
Quadrant IV is the bottom right quadrant on the coordinate plane. In this quadrant, both the x and y coordinates are positive. However, since the x-coordinate of the given point is 0, it does not lie in quadrant IV.
b) On the positive direction of y-axis:
The positive direction of the y-axis is the upward direction. Since the y-coordinate of the given point is 9, which is positive, it lies on the positive direction of the y-axis. Therefore, option 'B' is correct.
c) In quadrant III:
Quadrant III is the bottom left quadrant on the coordinate plane. In this quadrant, the x-coordinate is negative, but the y-coordinate is positive. Since the x-coordinate of the given point is 0, it does not lie in quadrant III.
d) On the positive direction of x-axis:
The positive direction of the x-axis is the rightward direction. However, since the x-coordinate of the given point is 0, it does not lie on the positive direction of the x-axis.
Therefore, the correct answer is option 'B' because the point (0, 9) lies on the positive direction of the y-axis.
The equation of x-axis is- a)y = x
- b)x = 0
- c)y = 0
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The equation of x-axis is
a)
y = x
b)
x = 0
c)
y = 0
d)
none of these
|
|
Jaideep Sharma answered |
**Explanation:**
The equation of the x-axis represents all the points that lie on the x-axis. The x-axis is a horizontal line that intersects the y-axis at the origin (0,0).
The equation of the x-axis can be written in the form y = k, where k is a constant. Since the x-axis is a horizontal line, the value of y remains constant for all values of x.
To find the equation of the x-axis, we need to determine the value of y that remains constant. At every point on the x-axis, the value of y is always 0. Therefore, the equation of the x-axis is y = 0.
**Option C: y = 0**
The equation of the x-axis represents all the points that lie on the x-axis. The x-axis is a horizontal line that intersects the y-axis at the origin (0,0).
The equation of the x-axis can be written in the form y = k, where k is a constant. Since the x-axis is a horizontal line, the value of y remains constant for all values of x.
To find the equation of the x-axis, we need to determine the value of y that remains constant. At every point on the x-axis, the value of y is always 0. Therefore, the equation of the x-axis is y = 0.
**Option C: y = 0**
The point (–2, 0) lies on :- a)+ve x-axis
- b)+ve y-axis
- c)–ve x-axis
- d)–ve y-axis
Correct answer is option 'C'. Can you explain this answer?
The point (–2, 0) lies on :
a)
+ve x-axis
b)
+ve y-axis
c)
–ve x-axis
d)
–ve y-axis
|
Debolina Iyer answered |
Explanation:
The point (–2, 0) lies on the –ve x-axis because of the following reasons:
Coordinate Plane:
- The coordinate plane consists of two perpendicular lines, the x-axis and y-axis, intersecting at the origin (0,0).
- The x-axis is the horizontal line where y=0, and the y-axis is the vertical line where x=0.
Understanding Coordinates:
- In the Cartesian coordinate system, points are represented as (x, y) where x is the horizontal distance from the y-axis (positive to the right, negative to the left) and y is the vertical distance from the x-axis (positive upwards, negative downwards).
Point Coordinates:
- The given point (–2, 0) has an x-coordinate of –2 and a y-coordinate of 0.
- This means the point is 2 units to the left of the y-axis (negative x-direction) and lies on the x-axis where y=0.
Conclusion:
- As the point lies on the x-axis at a negative x-coordinate of –2, it is located on the –ve x-axis.
- Therefore, the correct option is –ve x-axis (option C).
The point (–2, 0) lies on the –ve x-axis because of the following reasons:
Coordinate Plane:
- The coordinate plane consists of two perpendicular lines, the x-axis and y-axis, intersecting at the origin (0,0).
- The x-axis is the horizontal line where y=0, and the y-axis is the vertical line where x=0.
Understanding Coordinates:
- In the Cartesian coordinate system, points are represented as (x, y) where x is the horizontal distance from the y-axis (positive to the right, negative to the left) and y is the vertical distance from the x-axis (positive upwards, negative downwards).
Point Coordinates:
- The given point (–2, 0) has an x-coordinate of –2 and a y-coordinate of 0.
- This means the point is 2 units to the left of the y-axis (negative x-direction) and lies on the x-axis where y=0.
Conclusion:
- As the point lies on the x-axis at a negative x-coordinate of –2, it is located on the –ve x-axis.
- Therefore, the correct option is –ve x-axis (option C).
The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is- a)(-3, 0)
- b)(0, 3)
- c)(0, -3)
- d)(3, 0)
Correct answer is option 'D'. Can you explain this answer?
The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is
a)
(-3, 0)
b)
(0, 3)
c)
(0, -3)
d)
(3, 0)
|
|
Nishi Kumari answered |
Because in co-ordinates x axis comes first as (x, y)
The point which lies on x-axis at a distance of 4 units in the negative direction of x-axis is
- a)(4, 0)
- b)(-4, 0)
- c)(0, 4)
- d)(0, -4)
Correct answer is option 'B'. Can you explain this answer?
The point which lies on x-axis at a distance of 4 units in the negative direction of x-axis is
a)
(4, 0)
b)
(-4, 0)
c)
(0, 4)
d)
(0, -4)
|
|
Zachary Foster answered |
To understand this, let's break down the information given:
- x-axis: The x-axis is the horizontal line in the coordinate plane. Any point on the x-axis will have a y-coordinate of 0 because it does not move up or down from the axis.
- Distance of 4 units in the negative direction of x-axis:
- The x-axis has a positive direction (towards the right) and a negative direction (towards the left).
- Moving 4 units in the negative direction means moving 4 units to the left from the origin (0,0).
- Coordinates:
- When you move 4 units to the left on the x-axis, the x-coordinate becomes -4, and since the point is on the x-axis, the y-coordinate remains 0.
Therefore, the point that lies on the x-axis 4 units in the negative direction is (−4,0)(-4, 0)(−4,0).
This corresponds to option (b) (-4, 0).
The point B(-3, 4) lies in
- a)IV Quadrant
- b)II Quadrant
- c)I Quadrant
- d)III Quadrant
Correct answer is option 'B'. Can you explain this answer?
The point B(-3, 4) lies in
a)
IV Quadrant
b)
II Quadrant
c)
I Quadrant
d)
III Quadrant
|
|
Purbasha Dutta answered |
Abscissa is negative and ordinate is positive
so it will lie in 2 quadrant
so it will lie in 2 quadrant
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Coordinate Geometry" are available for CBSE Class 9 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 9 Mathematics (Maths)Q The point of intersection of X and Y axes is called :- a)Origin
- b)Null point
- c)Common point
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Coordinate Geometry" are available for CBSE Class 9 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 9 Mathematics (Maths)
Q The point of intersection of X and Y axes is called :
a)
Origin
b)
Null point
c)
Common point
d)
None of these
|
Samaira Kapoor answered |
Explanation:
- The point where X and Y axes intersect is known as the origin.
- It is denoted by the letter 'O'.
- The coordinates of the origin are (0,0).
- The X-axis is the horizontal line that runs from left to right.
- The Y-axis is the vertical line that runs from top to bottom.
- Together, they form a rectangular coordinate system, also known as a Cartesian coordinate system.
- The coordinates of a point in this system are given by an ordered pair (x, y) where x represents the distance from the origin along the X-axis and y represents the distance from the origin along the Y-axis.
- The origin is an important point in mathematics and is used as a reference point for many calculations and geometric constructions.
The point C(-5, -2) lies in- a)III Quadrant
- b)IV Quadrant
- c)I Quadrant
- d)II Quadrant
Correct answer is option 'A'. Can you explain this answer?
The point C(-5, -2) lies in
a)
III Quadrant
b)
IV Quadrant
c)
I Quadrant
d)
II Quadrant
|
Nisha Nair answered |
Explanation:
Quadrants in the Coordinate Plane:
In the coordinate plane, there are four quadrants labeled as I, II, III, and IV. The quadrants are separated by the x-axis and y-axis. The signs of the x and y coordinates determine in which quadrant a point lies.
Coordinates of the Point:
The point C(-5, -2) has x-coordinate as -5 and y-coordinate as -2.
Identification of Quadrant:
To determine in which quadrant the point C(-5, -2) lies, we need to consider the signs of the x and y coordinates.
- Since the x-coordinate is negative (-5), it means the point lies to the left of the y-axis.
- Since the y-coordinate is negative (-2), it means the point lies below the x-axis.
Location of Point C:
Based on the signs of the coordinates:
- The point C(-5, -2) lies to the left of the y-axis (negative x-coordinate).
- The point C(-5, -2) lies below the x-axis (negative y-coordinate).
Conclusion:
Therefore, the point C(-5, -2) lies in the III Quadrant of the coordinate plane.
Quadrants in the Coordinate Plane:
In the coordinate plane, there are four quadrants labeled as I, II, III, and IV. The quadrants are separated by the x-axis and y-axis. The signs of the x and y coordinates determine in which quadrant a point lies.
Coordinates of the Point:
The point C(-5, -2) has x-coordinate as -5 and y-coordinate as -2.
Identification of Quadrant:
To determine in which quadrant the point C(-5, -2) lies, we need to consider the signs of the x and y coordinates.
- Since the x-coordinate is negative (-5), it means the point lies to the left of the y-axis.
- Since the y-coordinate is negative (-2), it means the point lies below the x-axis.
Location of Point C:
Based on the signs of the coordinates:
- The point C(-5, -2) lies to the left of the y-axis (negative x-coordinate).
- The point C(-5, -2) lies below the x-axis (negative y-coordinate).
Conclusion:
Therefore, the point C(-5, -2) lies in the III Quadrant of the coordinate plane.
If x = y then (x,y) = (y,x).- a)The above statement is TRUE
- b)The above statement is TRUE if x is not equal to y
- c)The above statement is FALSE
- d)The above statement is TRUE if x is less then y
Correct answer is option 'A'. Can you explain this answer?
If x = y then (x,y) = (y,x).
a)
The above statement is TRUE
b)
The above statement is TRUE if x is not equal to y
c)
The above statement is FALSE
d)
The above statement is TRUE if x is less then y
|
Prisha Behera answered |
Suppose x=5
So, y=5
Then, (5,5)=(5,5)
A point both of whose co-ordinates are positive lies in- a)quadrant III only
- b)quadrant I only
- c)quadrant I and III
- d)quadrant II and IV
Correct answer is option 'B'. Can you explain this answer?
A point both of whose co-ordinates are positive lies in
a)
quadrant III only
b)
quadrant I only
c)
quadrant I and III
d)
quadrant II and IV
|
|
Sayali Shah answered |
**Explanation:**
To understand why the correct answer is option 'B', let's first review the four quadrants on the coordinate plane:
1. **Quadrant I:** It is located in the upper right portion of the coordinate plane where both the x-coordinate (horizontal) and y-coordinate (vertical) are positive.
2. **Quadrant II:** It is located in the upper left portion of the coordinate plane where the x-coordinate is negative and the y-coordinate is positive.
3. **Quadrant III:** It is located in the lower left portion of the coordinate plane where both the x-coordinate and y-coordinate are negative.
4. **Quadrant IV:** It is located in the lower right portion of the coordinate plane where the x-coordinate is positive and the y-coordinate is negative.
Now, let's consider a point with both coordinates positive. This means that the x-coordinate is positive (greater than 0) and the y-coordinate is also positive (greater than 0).
Since the x-coordinate is positive, the point cannot lie in Quadrants II or III, as these quadrants have negative x-coordinates. Therefore, the point must lie in either Quadrant I or Quadrant IV.
However, since the y-coordinate is also positive, the point cannot lie in Quadrant IV, as this quadrant has a negative y-coordinate. Therefore, the only quadrant where a point with both positive coordinates can lie is Quadrant I.
Hence, the correct answer is option 'B' - the point lies in Quadrant I only.
To understand why the correct answer is option 'B', let's first review the four quadrants on the coordinate plane:
1. **Quadrant I:** It is located in the upper right portion of the coordinate plane where both the x-coordinate (horizontal) and y-coordinate (vertical) are positive.
2. **Quadrant II:** It is located in the upper left portion of the coordinate plane where the x-coordinate is negative and the y-coordinate is positive.
3. **Quadrant III:** It is located in the lower left portion of the coordinate plane where both the x-coordinate and y-coordinate are negative.
4. **Quadrant IV:** It is located in the lower right portion of the coordinate plane where the x-coordinate is positive and the y-coordinate is negative.
Now, let's consider a point with both coordinates positive. This means that the x-coordinate is positive (greater than 0) and the y-coordinate is also positive (greater than 0).
Since the x-coordinate is positive, the point cannot lie in Quadrants II or III, as these quadrants have negative x-coordinates. Therefore, the point must lie in either Quadrant I or Quadrant IV.
However, since the y-coordinate is also positive, the point cannot lie in Quadrant IV, as this quadrant has a negative y-coordinate. Therefore, the only quadrant where a point with both positive coordinates can lie is Quadrant I.
Hence, the correct answer is option 'B' - the point lies in Quadrant I only.
Point P(x,y) is a point in the third quadrant of the Cartesian plane. Then- a)x and y both are positive
- b)x and y both are negative
- c)x is negative and y is positive
- d)x is positive and y is negative
Correct answer is 'B'. Can you explain this answer?
Point P(x,y) is a point in the third quadrant of the Cartesian plane. Then
a)
x and y both are positive
b)
x and y both are negative
c)
x is negative and y is positive
d)
x is positive and y is negative
|
|
Himaja Ammu answered |
Both r negative 1st quadrant:(+,+) 2nd quadrant:(-,+) 3rd quadrant:(-,-) 4th quadrant:(+,-)
The distance of a point (-5, 6) from the y- axis is
- a)6 units
- b)5 units
- c)1 unit
- d)-5 units
Correct answer is option 'B'. Can you explain this answer?
The distance of a point (-5, 6) from the y- axis is
a)
6 units
b)
5 units
c)
1 unit
d)
-5 units
|
|
Simran Yadav answered |
the distance of the point (-5, 6) from y- axis is |-5| units.
In general, the distance of the point (x,y) from x-axis is y and from y-axis is x.
The equation of y-axis is- a)y = x
- b)y = 0
- c)x = 0
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The equation of y-axis is
a)
y = x
b)
y = 0
c)
x = 0
d)
none of these
|
|
Vicky Singh answered |
Equation of y-axis which means x=0
The perpendicular distance of a point Q(4, 7) from y-axis is- a)4 units
- b)7 units
- c)11 units
- d)3 units
Correct answer is option 'A'. Can you explain this answer?
The perpendicular distance of a point Q(4, 7) from y-axis is
a)
4 units
b)
7 units
c)
11 units
d)
3 units
|
Arka Dey answered |
(i) In the first quadrant, the coordinates of the required point will be (5,4).
(ii) In the second quadrant, the coordinates of the required point will be (-5,4).
(iii) In the third quadrant, the coordinates of the required point will be (-5,-4).
(iv) In the fourth quadrant, the coordinates of the required point will be (5,-4)
The point (0, 3) lies on :- a)+ve x-axis
- b)+ve y-axis
- c)–ve x-axis
- d)–ve y-axis
Correct answer is 'B'. Can you explain this answer?
The point (0, 3) lies on :
a)
+ve x-axis
b)
+ve y-axis
c)
–ve x-axis
d)
–ve y-axis
|
|
Tarun Bhaskar answered |
This is because y is also called X=0 and x=0,y=3 so it will lie on positive y axis(+ve y axis)
From the given diagram, the coordinates of point P are ______.
- a)(-2, 3)
- b)(2, -3)
- c)(2, 3)
- d)(-3, 2)
Correct answer is option 'B'. Can you explain this answer?
From the given diagram, the coordinates of point P are ______.
a)
(-2, 3)
b)
(2, -3)
c)
(2, 3)
d)
(-3, 2)
|
C K Academy answered |
We can see in diagram that distance of point P is 2 from y – axis in positive x – axis direction and 3 from x – axis but in negative y – axis direction.
Therefore, x – coordinate and y – coordinate of point p will be 2 and -3 respectively.
Coordinates of any points are shown in (x – coordinate, y – coordinate) form.
Therefore, coordinates of point P are (2, -3).
Therefore, x – coordinate and y – coordinate of point p will be 2 and -3 respectively.
Coordinates of any points are shown in (x – coordinate, y – coordinate) form.
Therefore, coordinates of point P are (2, -3).
The co-ordinates of the origin are- a)(2, 0)
- b)(0, 2)
- c)(0, 0)
- d)(2, 2)
Correct answer is option 'C'. Can you explain this answer?
The co-ordinates of the origin are
a)
(2, 0)
b)
(0, 2)
c)
(0, 0)
d)
(2, 2)
|
EduRev Class 9 answered |
The origin in any standard coordinate system is the point where both the x and y values are zero. Therefore, its coordinates are (0, 0). This makes option C the correct answer.
Abscissa of all points on the x-axis is- a)-1
- b)0
- c)any number
- d)1
Correct answer is option 'C'. Can you explain this answer?
Abscissa of all points on the x-axis is
a)
-1
b)
0
c)
any number
d)
1
|
|
EduRev Class 9 answered |
The abscissa of a point refers to its x-coordinate in the Cartesian coordinate system.
- On the x-axis, the y-coordinate (ordinate) is always 0, while the x-coordinate (abscissa) can be any real number.
- This means that any point on the x-axis is of the form (x, 0), where x can be any number.
Thus, the correct answer is:
c) any number.
Abscissa of a point is negative in- a)quadrant IV only
- b)quadrant II and III
- c)quadrant I only
- d)quadrant I and IV
Correct answer is option 'B'. Can you explain this answer?
Abscissa of a point is negative in
a)
quadrant IV only
b)
quadrant II and III
c)
quadrant I only
d)
quadrant I and IV
|
Aruna Singh answered |
The correct answer is:
quadrant II and III
In a two-dimensional coordinate system, the abscissa of a point refers to the distance of the point from the y-axis. If the abscissa of a point is negative, it means that the point is located to the left of the y-axis. This occurs in quadrants II and III of the coordinate plane.
In quadrant II, both the x-coordinate (abscissa) and y-coordinate are negative. In quadrant III, the x-coordinate is negative and the y-coordinate is positive.
In quadrant I, the abscissa is positive, as the point is located to the right of the y-axis. In quadrant IV, both the x-coordinate and y-coordinate are negative, so the abscissa is also negative.
Therefore, the correct answer is quadrant II and III.
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