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Test: Coordinate Geometry - 2 - Class 9 MCQ


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25 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Coordinate Geometry - 2

Test: Coordinate Geometry - 2 for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation. The Test: Coordinate Geometry - 2 questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Coordinate Geometry - 2 MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Coordinate Geometry - 2 below.
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Test: Coordinate Geometry - 2 - Question 1

The point of intersection of X and Y axes is called :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 1

The point at which X and Y axes intersect is known as the origin.
The origin is shown in the diagram below:

The origin is the point where the axes intersect. At this point the x-coordinate and y-coordinate both are zero.

Test: Coordinate Geometry - 2 - Question 2

The point (2, 3) is at a distance of _______________ units from x-axis :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 2

The distance between the point (2, 3) and x-axis can be determined by assuming a point (2, 0) on x-axis.
The distance between 
Therefore, the distance between (2, 3) and (2, 0)​​​​​​​ 

Hence, the distance of the point (2, 3) from x-axis is 3 units.

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Test: Coordinate Geometry - 2 - Question 3

The point (3, 2) is at a distance of _______________ units from y-axis :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 3

Test: Coordinate Geometry - 2 - Question 4

The point (–3, 2) belongs to Quadrant _______________ :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 4

The point (–3, 2) is located in the second quadrant. This is because the x coordinate is negative and the y coordinate is positive, which are the characteristics of points in Quadrant II.

The correct answer is: B: Q2

Test: Coordinate Geometry - 2 - Question 5

The point (2, –3) belongs to quadrant _______________ :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 5

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 (+,−)

Test: Coordinate Geometry - 2 - Question 6

The point (3, 2) belongs to quadrant _______________ :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 6

The point (3, 2) is located in the first quadrant. This is because both the x coordinate and the y coordinate are positive, which are the characteristics of points in Quadrant I.
The correct answer is: A: Q1

Test: Coordinate Geometry - 2 - Question 7

The point (–2, –3) belongs to Quadrant :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 7

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

Test: Coordinate Geometry - 2 - Question 8

The point (–2, 0) lies on :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 8

The point (−2, 0) lies on the negative x-axis because the x coordinate is negative and the y coordinate is zero, indicating a location along the x-axis to the left of the origin.

The correct answer is: C: –ve x-axis

Test: Coordinate Geometry - 2 - Question 9

The point (0, –2) lies on :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 9

The point (0, −2) lies on the negative y-axis because the x coordinate is zero and the y coordinate is negative, indicating a location along the y-axis below the origin.

The correct answer is: D: –ve y-axis

Test: Coordinate Geometry - 2 - Question 10

The point (3, 0) lies on :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 10

The point (3, 0) lies on the positive x-axis because the x coordinate is positive and the y coordinate is zero, indicating a location along the x-axis to the right of the origin.

The correct answer is: A: +ve x-axis

Test: Coordinate Geometry - 2 - Question 11

The point (0, 3) lies on :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 11

The point (0, 3) lies on the positive y-axis because the x coordinate is zero and the y coordinate is positive, indicating a location along the y-axis above the origin.

The correct answer is: B: +ve y-axis

Test: Coordinate Geometry - 2 - Question 12

The distance between the points (–4, 7) and (1, –5) is :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 12

Use the distance formula to determine the distance between two points.

√{1 - (-4)}2 + {(-5) - 7}2

= √25 + 144

= √169

= 13

Test: Coordinate Geometry - 2 - Question 13

The distance of the point (–2, –2) from the origin is :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 13
Solving it by Pythagoras theorem the perpendicular will be 2 and the base will also be 2 the distance will be the hypotenuse =>. h² = b² + p² h²= 2² + 2² h² = 4+4 h²= 8 h=√8 √8 can be written as √2 x √2 x √2 which is equal to 2√2units.
Test: Coordinate Geometry - 2 - Question 14

If the distance between points (p, –5), (2, 7) is 13 units, then p is _____________ :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 14

Given, the distance between points (p, -5) and (2, 7) is 13 units.
∵ The distance between two points (x1, y1) and (x2, y2) is 

⇒ (2 − p)2 + (7 + 5)2 = 132

⇒ (2 − p)2 = 169 − 144

⇒ (2 − p)2 = 25

⇒ 2 − p = ±5

case 1:
2 − p = 5 ⇒ p = −3

case 2:
2 − p = −5 ⇒ p = 7

Hence, p can be -3 or 7

Test: Coordinate Geometry - 2 - Question 15

The points (a, a) (-a, -a) and (-a(√3), (a√3)) form the vertices of an :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 15

The given points are let

⇒ ΔABC is an equilateral triangle.
Hence proved.

Test: Coordinate Geometry - 2 - Question 16

Find the ratio in which the line joining the points (6, 4) and (1, –7) is divided by x-axis.

Detailed Solution for Test: Coordinate Geometry - 2 - Question 16

Test: Coordinate Geometry - 2 - Question 17

The points (2, –1), (3, 4), (–2, 3) and (–3, –2) taken in the order from the vertices of _________________:

Detailed Solution for Test: Coordinate Geometry - 2 - Question 17

In rhombus, all sides are equal and diagonals are not equal.

Distance between two points = [(x2−x1)2 + (y2−y1)2]1/2

AB =  [(3−2)2 + (4+1)2]1/2 =(26)1/2

BC = [(3+2)2 + (3−4)2]1/2 = (26)1/2

CD = [(-3+2)2 + (-2-3)2]1/2 = (26)1/2

DA = [(-3-2)2 + (-2+1)2]1/2 = (26)1/2

AC = [(2+2)2 + (4)2]1/2 = 4(2)1/2

BD = [(-3-3)2 + (4+2)2]1/2 = 6(2)1/2

AB=BC=CD=DA All sides are equal

AC and BD Diagonals are not equal

Test: Coordinate Geometry - 2 - Question 18

The points (0, 0), (–2, 0) and (3, 0) _________________:

Detailed Solution for Test: Coordinate Geometry - 2 - Question 18

The points (0, 0), (–2, 0) and (3, 0) all have their Y-coordinates as zero and different x-coordinates, indicating they are positioned along the x-axis. Additionally, because they are on the same line (the x-axis), they are collinear.

The correct answer is: D: Both A and B

Test: Coordinate Geometry - 2 - Question 19

The point on Y-axis equidistant from (–3, 4) and (7, 6) is _________________:

Detailed Solution for Test: Coordinate Geometry - 2 - Question 19

The point on the Y-axis that is equidistant from the points (–3, 4) and (7, 6) can be found using the distance formula.

The distance between the two points is √(7- (-3))² + (6-4)² = √(10² + 2²) = √(100 + 4) = √104 = 10.2.

The point on the Y-axis that is equidistant from the two points is (0, 10.2).

The closest answer to this is (0, 15).

Test: Coordinate Geometry - 2 - Question 20

The point on X-axis equidistant from (5, 4) and (–2, 3) is _________________:

Detailed Solution for Test: Coordinate Geometry - 2 - Question 20

Test: Coordinate Geometry - 2 - Question 21

The points on X-axis at a distance of 10 units from (11, –8) are :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 21

Let P(x, 0) be the point on the x-axis. Then as per the question we have

AP = 10

Hence, the points on the x-axis are (5, 0) and (17,0) .

Test: Coordinate Geometry - 2 - Question 22

The points on Y-axis at a distance of 13 units from point (–5, 7) are :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 22
Let  P(0,y) be the required point on y−axis.
Now, distance between the point P(0,y) and A(−5,7) is 13 units.
Now, PA = 13 units
⇒√(0+5)^2 + (y−7)^2 = 13
⇒√25 + y2 + 49 − 14y = 13
⇒√y^2 + 74 − 14y = 13
⇒y^2 − 14y + 74 = 169
⇒y^2 − 14y − 95 = 0
⇒y^2 − 19y + 5y − 95 = 0
⇒y(y−19) + 5(y−19) = 0
⇒(y+5)(y−19) = 0⇒y+5 = 0   or  y−19 = 0
⇒y = −5   or  y = 19
So, the required points are :(0,−5) and (0,19)
Test: Coordinate Geometry - 2 - Question 23

The coordinates of the centre of a circle passing through (1, 2), (3, –4) and (5, –6) is _________________:

Detailed Solution for Test: Coordinate Geometry - 2 - Question 23

Given three points (1,2),(3,−4)and(5,−6)

Let the coordinates o centre be O(h,k)

The distance from the centre to a point on the circumference is equal to radius.

∴ OA=OB=OC

From distance formula 

OA2=OB2

 

Test: Coordinate Geometry - 2 - Question 24

The points (–5, 6), (3, 0) and (9, 8) form the vertices of :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 24

Let the given points be A(-5, 6), B(3, 0) and C(9, 8).

Therefore,  AB =  BC = units 

This show that  Δ ABC  is right angled at B. Therefore, the points A(-5,6), B(3,0) and C(9,8). are the vertices of an isosceles rightangled triangle
Also, area of a triangle = 1/2 x base x height
If AB is the height and BC is the base,
Area = 1/2 x 10 x 10
= 50 square units

Test: Coordinate Geometry - 2 - Question 25

The points (4, 4), (3, 5) and (–1, –1) from the vertices of :

Detailed Solution for Test: Coordinate Geometry - 2 - Question 25

The vertices of the given triangles are A(4, 4), B (3, 5) and C (- 1, - 1).

It is known that the slope (m) of a non-vertical line passing through the points (x₁, y₁) and (x₂, y₂) is given by m = (y₂ - y₁)/(x₂ - x₁), x2 ≠ x₁

Therefore, slope of AB (m₁) = (5 - 4)/(3 - 4) = - 1

Slope of BC (m₂) = (- 1 - 5)/(- 1 - 3) = - 6/- 4 = 3/2

Slope of CA (m₃) = (4 + 1)/(4 + 1) = 5/5 = 1

It is observed that m₁m₃ = - 1

This shows that line segments AB and CA are perpendicular to each other i.e., the given triangle is right-angled at A(4, 4).

Thus, the points (4, 4), (3, 5) and (- 1, - 1) are the vertices of a right-angled triangle

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