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All questions of Coordinate Geometry for Class 10 Exam
The distance of the point P (2, 3) from the x-axis is
- a)2
- b)3
- c)1
- d)5
Correct answer is option 'B'. Can you explain this answer?
The distance of the point P (2, 3) from the x-axis is
a)
2
b)
3
c)
1
d)
5
|
Kamna Science Academy answered |
To find the distance of point P(2, 3) from the x-axis:
- The distance from a point (x, y) to the x-axis is the absolute value of the y-coordinate.
- For point P(2, 3), the y-coordinate is 3.
- Therefore, the distance of point P from the x-axis is 3.
- Hence, the correct answer is B: 3.
- The distance from a point (x, y) to the x-axis is the absolute value of the y-coordinate.
- For point P(2, 3), the y-coordinate is 3.
- Therefore, the distance of point P from the x-axis is 3.
- Hence, the correct answer is B: 3.
The distance of the point P (-6, 8) from the origin is- a)8
- b)2√7
- c)10
- d)6
Correct answer is option 'C'. Can you explain this answer?
The distance of the point P (-6, 8) from the origin is
a)
8
b)
2√7
c)
10
d)
6
|
|
Nirmal Kumar answered |
Let A(-6,8) and B(0,0),
by distance formula-->
distance between A and B=
√(x1-x2)²+(y1-y2)²,
=√(-6-0)²+(8-0)²,
=√(36)+(64),
=√100=10
by distance formula-->
distance between A and B=
√(x1-x2)²+(y1-y2)²,
=√(-6-0)²+(8-0)²,
=√(36)+(64),
=√100=10
The points (k + 1, 1), (2k + 1, 3) and (2k + 2, 2k) are collinear if- a)k = - 1, 2
- b)
- c)k = 2, 1
- d)
Correct answer is option 'D'. Can you explain this answer?
The points (k + 1, 1), (2k + 1, 3) and (2k + 2, 2k) are collinear if
a)
k = - 1, 2
b)
c)
k = 2, 1
d)
|
Kiran Mehta answered |
∵ Points are collinear.
∴ (k + 1) (3 - 2k) + (2k, + 1) (2k - 1) + (2k + 2) (1 - 3) = 0
⇒ 3k+3 - 2k2 - 2k + 4k2 - 1 - 4k - 4 = 0 ⇒ 2k2 - 3k - 2 = 0
⇒ 2k2 - 4k + k - 2 = 0
⇒ 2k(k - 2) + 1(k - 2) = 0
⇒ (2k + 1) (k - 2) = 0
∴ (k + 1) (3 - 2k) + (2k, + 1) (2k - 1) + (2k + 2) (1 - 3) = 0
⇒ 3k+3 - 2k2 - 2k + 4k2 - 1 - 4k - 4 = 0 ⇒ 2k2 - 3k - 2 = 0
⇒ 2k2 - 4k + k - 2 = 0
⇒ 2k(k - 2) + 1(k - 2) = 0
⇒ (2k + 1) (k - 2) = 0
The distance between the points A (0, 6) and B (0, -2) is- a)6
- b)8
- c)4
- d)2
Correct answer is option 'B'. Can you explain this answer?
The distance between the points A (0, 6) and B (0, -2) is
a)
6
b)
8
c)
4
d)
2
|
Amit Kumar answered |
Since both these points lie on a straight line i.e x axis, distance will be the difference between the respective y coordinates
(0,-2) & (0,6) => 6-(-2)) = 6+2 = 8
(0,-2) & (0,6) => 6-(-2)) = 6+2 = 8
The graph of the equation x = 3 is:- a)a point
- b)straight line parallel to y axis
- c)straight line passing through the origin
- d)straight line parallel to x axis
Correct answer is option 'B'. Can you explain this answer?
The graph of the equation x = 3 is:
a)
a point
b)
straight line parallel to y axis
c)
straight line passing through the origin
d)
straight line parallel to x axis
|
Naina Sharma answered |
x=3 is fixed. This means the value of x is constant. So y can vary but x has only one value. For example (3,0),(3,2),(3,5) etc. So the line drawn will be parallel to y axis as y can vary.
If the distance between the points (2, - 2) and (-1, x) is 5, one of the values of x is
- a)-2
- b)2
- c)-1
- d)1
Correct answer is option 'B'. Can you explain this answer?
If the distance between the points (2, - 2) and (-1, x) is 5, one of the values of x is
a)
-2
b)
2
c)
-1
d)
1
|
|
Naina Sharma answered |
Let us consider the points as
A = (2, -2)
B = (-1, x)
AB = 5 units
Using the distance formula
AB2 = (x₂ - x₁)2 + (y₂ - y₁)2
Substituting the values
52 = (-1 - 2)2 + (x + 2)2
25 = (-3)2 + (x + 2)2
Using the algebraic identity
(a + b)2 = a2 + b2 + 2ab
25 = 9 + x2 + 4 + 4x
By further calculation
25 = x2 + 4x + 13
x2 + 4x + 13 - 25 = 0
x2 + 4x - 12 = 0
By splitting the middle term
x2 + 6x - 2x - 12 = 0
Taking out the common terms
x(x + 6) - 2(x + 6) = 0
(x + 6)(x - 2) = 0
So we get
x + 6 = 0
x = -6
And
x - 2 = 0
x = 2
The end points of diameter of circle are (2, 4) and (-3, -1). The radius of the circle is
- a)
- b)5√2
- c)3√2
- d)
Correct answer is option 'A'. Can you explain this answer?
The end points of diameter of circle are (2, 4) and (-3, -1). The radius of the circle is
a)
b)
5√2
c)
3√2
d)
|
Nk Classes answered |
radius = Diameter/2
diameter = √((2-(-3))2 + (4-(-1))2)
= √52+52 = √50 = 5√2
The distance between the points A (0, 7) and B (0, -3) is- a)4 units
- b)10 units
- c)7 units
- d)3 units
Correct answer is option 'B'. Can you explain this answer?
The distance between the points A (0, 7) and B (0, -3) is
a)
4 units
b)
10 units
c)
7 units
d)
3 units
|
|
Amit Sharma answered |
Since both these points lie on a straight line i.e x axis, distance will be the difference between the respective y coordinates
(0,-3) (0,7)
7-(-3) = 7+3 = 10
The line segment joining (2, – 3) and (5, 6) is divided by x-axis in the ratio:- a)2 : 1
- b)3 : 1
- c)1 : 2
- d)1 : 3.
Correct answer is option 'A'. Can you explain this answer?
The line segment joining (2, – 3) and (5, 6) is divided by x-axis in the ratio:
a)
2 : 1
b)
3 : 1
c)
1 : 2
d)
1 : 3.
|
|
Krishna Iyer answered |
Hence, the ratio is 1:2 and the division is internal.
If P(1, 2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then- a)a = 2, b = 4
- b)a = 3, b = 4
- c)a = 2, b = 3
- d)a = 3, b = 5
Correct answer is option 'C'. Can you explain this answer?
If P(1, 2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then
a)
a = 2, b = 4
b)
a = 3, b = 4
c)
a = 2, b = 3
d)
a = 3, b = 5
|
Manasa Deshpande answered |
PQRS is a parallelogram if and only if the mid point of the diagonals PR is same as that of the mid point of Q, S. That is, if and only if
units from origin
units from origin
The point on x-axis which is equidistant from (5,9) and (-4,6) is- a)(3,0)
- b)(1,0)
- c)(2,0)
- d)(4,1)
Correct answer is option 'A'. Can you explain this answer?
The point on x-axis which is equidistant from (5,9) and (-4,6) is
a)
(3,0)
b)
(1,0)
c)
(2,0)
d)
(4,1)
|
Vikas Kumar answered |
for 2 points to be equidistant to 2 another the length of the line drawn to them should the first two should be equal to the next two.
let that point be (x,0) (y=0 as it leis on the x axis)
using distance formula-
root of ((x+4)2 +(0-6)2)=root of ((x-5)2 +(0-9)2)
squaring both sides and opening the brackets we get-
x2 + 8x + 16 + 36 = x2 - 10x + 25 +81
bring variables to one side and constants to another we get-
18x = 54
x = 54/18 = 3
therefore x = 3 and y =0 (since it leis in the x axis)
The points A (9, 0), B (9, 6), C (-9, 6) and D (-9, 0) are the vertices of a- a)square
- b)rectangle
- c)rhombus
- d)trapezium
Correct answer is option 'B'. Can you explain this answer?
The points A (9, 0), B (9, 6), C (-9, 6) and D (-9, 0) are the vertices of a
a)
square
b)
rectangle
c)
rhombus
d)
trapezium
|
Pratibha das answered |
Here is the solution to your question:
Since,
• Opposite sides are equal
• Sides are perpendicular to each other
Therefore, ABCD is a rectangle
So, the correct answer is B.
You can learn everything about Coordinate Geometry for Class 10 through the link:
Therefore, ABCD is a rectangle
So, the correct answer is B.
You can learn everything about Coordinate Geometry for Class 10 through the link:
The values of x and y, if the distance of the point (x,y) from (-3,0) as well as from (3,0) is 4 are- a)x = 1, y = 7
- b)x = 2, y = 7
- c)x = 0, y = – √7
- d)x = 0, y = ± √7
Correct answer is option 'D'. Can you explain this answer?
The values of x and y, if the distance of the point (x,y) from (-3,0) as well as from (3,0) is 4 are
a)
x = 1, y = 7
b)
x = 2, y = 7
c)
x = 0, y = – √7
d)
x = 0, y = ± √7
|
|
Nisha Choudhury answered |
Given, the distance of point P(x, y ) from A(– 3, 0) and B(3, 0) is 4 units.
The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is √10, then the coordinates of the point are- a)(1,2) or (3,6)
- b)(1,2) or (3,5)
- c)(2,1) or (3,6)
- d)(2,1) or (6,3)
Correct answer is option 'A'. Can you explain this answer?
The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is √10, then the coordinates of the point are
a)
(1,2) or (3,6)
b)
(1,2) or (3,5)
c)
(2,1) or (3,6)
d)
(2,1) or (6,3)
|
|
Rahul Kapoor answered |
let the coordinate of that point be P(x,2x).
let the given point (4,3) be Q(4,3).
Then PQ=
The point (-1,-5) lies in the Quadrant- a)3rd
- b)1st
- c)2nd
- d)4th
Correct answer is option 'A'. Can you explain this answer?
The point (-1,-5) lies in the Quadrant
a)
3rd
b)
1st
c)
2nd
d)
4th
|
|
Rising Star answered |
Quadrant 1 = +,+
Quadrant 2= -,+
Quadrant 3= -,-
Quadrant 4 = +,-
Thus,the point (-1,-5 ) will lie in Quadrant 3 !!!
Quadrant 2= -,+
Quadrant 3= -,-
Quadrant 4 = +,-
Thus,the point (-1,-5 ) will lie in Quadrant 3 !!!
is the mid-point of the line segment joining the points Q (-6, 5) and E (-2, 3), then the value of a is
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.
Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.
a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true but R is NOT the correct explanation of A
c)
A is true but R is false
d)
A is false and R is True
|
|
Radha Iyer answered |
In case of assertion: Distance between two points (x1, y1) and (x2, y2) is given as,
where, (x1, y1) = (4, p)
(x2, y2) = (1, 0)
And, d = 5
Put the values, we have
52 = (1 − 4)2 + (0 – p)2
25 = (–3)2 + (–p)2
25 – 9 = p2
16 = p2
+4, –4 = p
∴ Assertion is incorrect.
In case of reason:
Let (x, y) be the point
Here, x1 = 7, y1 = –6, x2 = 3, y2 = 4, m = 1 and n = 2
So, the required point 
lies in IVth quadrant.
lies in IVth quadrant.∴ Reason is correct.
Hence, assertion is incorrect but reason is correct.
For the triangle whose sides are along the lines y = 15, 3x – 4y = 0, 5x + 12y = 0, the incentre is :- a)(1, 8)
- b)(8, 1)
- c)(-1, 8)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
For the triangle whose sides are along the lines y = 15, 3x – 4y = 0, 5x + 12y = 0, the incentre is :
a)
(1, 8)
b)
(8, 1)
c)
(-1, 8)
d)
None of these
|
|
Raghav Bansal answered |
Given equations:
3x – 4y = 0 …(1)
5x+12y = 0 …(2)
Y-15 = 0 …(3)
From the given equations, (1), (2) and (3) represent the sides AB, BC and CA respectively.
Solving (1) and (2), we get
x= 0, and y= 0
Therefore, the side AB and BC intersect at the point B (0, 0)
Solving (1) and (3), we get
x= 20, y= 15
Hence, the side AB and CA intersect at the point A (20, 15)
Solving (2) and (3), we get
x= -36, y = 15
Thus, the side BC and CA intersect at the point C (-36, 15)
Now,
BC = a = 39
CA = b = 56
AB = c = 25
Similarly, (x1, y1) = A(20, 15)
CA = b = 56
AB = c = 25
Similarly, (x1, y1) = A(20, 15)
(x2, y2) = B(0, 0)
(x3, y3) = C(-36, 15)
(x3, y3) = C(-36, 15)
Therefore, incentre is
A triangle with vertices (4, 0), (- 1, - 1) and (3, 5) is a/an- a)equilateral triangle
- b)right-angled triangle
- c)isosceles right-angled triangle
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
A triangle with vertices (4, 0), (- 1, - 1) and (3, 5) is a/an
a)
equilateral triangle
b)
right-angled triangle
c)
isosceles right-angled triangle
d)
none of these
|
Ananya Kumar answered |
A(4, 0), B(-1, -1), C(3, 5) are the vertices of a triangle. Then
Thus, the triangle is isosceles and right angle triangle.
The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) is- a)√2 + 1
- b)1 ± √2
- c)2 + √2
- d)3
Correct answer is option 'C'. Can you explain this answer?
The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) is
a)
√2 + 1
b)
1 ± √2
c)
2 + √2
d)
3
|
|
Nisha Choudhury answered |
Consider A (0,0),B (1,0),C (0,1)
=>AB=root(X2-X1)^2+(Y2-Y1)^2
=>AB=root (1-0)^2+(1-0)^2
=>AB=1
similarly,
BC=root2
and
AC=1
Perimeter=AB+BC+AC
=1+root1+1
=2+root2
If A and B are the points (-6, 7) and (-1, -5) respectively, then the distance 2AB is equal to- a)26
- b)169
- c)13
- d)238
Correct answer is option 'A'. Can you explain this answer?
If A and B are the points (-6, 7) and (-1, -5) respectively, then the distance 2AB is equal to
a)
26
b)
169
c)
13
d)
238
|
|
Aditi bajaj answered |
To find the distance between two points, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and allows us to calculate the distance between two points in a coordinate plane.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, we are given the points A (-6, 7) and B (-1, -5). We need to find the distance 2AB, which means we need to find the distance between A and B and then multiply it by 2.
Let's calculate the distance between A and B first:
x1 = -6, y1 = 7 (coordinates of A)
x2 = -1, y2 = -5 (coordinates of B)
Using the distance formula:
dAB = sqrt((-1 - (-6))^2 + (-5 - 7)^2)
= sqrt(5^2 + (-12)^2)
= sqrt(25 + 144)
= sqrt(169)
= 13
Now, to find the distance 2AB, we multiply the distance between A and B by 2:
2AB = 2 * 13
= 26
So, the distance 2AB is equal to 26. Therefore, the correct answer is option A.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, we are given the points A (-6, 7) and B (-1, -5). We need to find the distance 2AB, which means we need to find the distance between A and B and then multiply it by 2.
Let's calculate the distance between A and B first:
x1 = -6, y1 = 7 (coordinates of A)
x2 = -1, y2 = -5 (coordinates of B)
Using the distance formula:
dAB = sqrt((-1 - (-6))^2 + (-5 - 7)^2)
= sqrt(5^2 + (-12)^2)
= sqrt(25 + 144)
= sqrt(169)
= 13
Now, to find the distance 2AB, we multiply the distance between A and B by 2:
2AB = 2 * 13
= 26
So, the distance 2AB is equal to 26. Therefore, the correct answer is option A.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Centroid of a triangle formed by the points (a, b) (b, c), and (c, a) is at origin, Then a + b + c = 0 .Reason : Centroid of a △ABC with vertices A (x1, y1), B(x2, y2) and C (x3, y3) is given by
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : Centroid of a triangle formed by the points (a, b) (b, c), and (c, a) is at origin, Then a + b + c = 0 .
Reason : Centroid of a △ABC with vertices A (x1, y1), B(x2, y2) and C (x3, y3) is given by
a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true but R is NOT the correct explanation of A
c)
A is true but R is false
d)
A is false and R is True
|
|
Avinash Patel answered |
Centroid of a triangle with vertices (a, b) (b, c), and (c, a) is
a + b + c = 0
he horizontal and vertical lines drawn to determine the position of a point in a Cartesian plane are called- a)Intersecting lines
- b)Transversals
- c)Perpendicular lines
- d)X-axis and Y-axis
Correct answer is option 'D'. Can you explain this answer?
he horizontal and vertical lines drawn to determine the position of a point in a Cartesian plane are called
a)
Intersecting lines
b)
Transversals
c)
Perpendicular lines
d)
X-axis and Y-axis
|
|
Ananya Das answered |
The point is determined on 2 dimensions .The name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane is x-axis and y-axis respectively. The name of each part of the plane formed by these two lines x-axis and the y-axis is quadrants. The point where these two lines intersect is called the origin.
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Coordinate Geometry" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths) Q. The distance between the points (a, b) and (– a, – b) is :- a)a2+b2
- b)
- c)0
- d)
Correct answer is option 'D'. Can you explain this answer?
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Coordinate Geometry" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)
Q. The distance between the points (a, b) and (– a, – b) is :
a)
a2+b2
b)
c)
0
d)
|
Flembe Academy answered |
We have distance formula as d = 
Where x1=a,y1=b,x2=-a,y2=-b
Where x1=a,y1=b,x2=-a,y2=-b
The condition that the point (x,y) may lie on the line joining (3,4) and (-5,-6) is- a)-5x+4y+1=0
- b)-5x-4y+1=0
- c)5x+4y+1=0
- d)5x-4y+1=0
Correct answer is option 'D'. Can you explain this answer?
The condition that the point (x,y) may lie on the line joining (3,4) and (-5,-6) is
a)
-5x+4y+1=0
b)
-5x-4y+1=0
c)
5x+4y+1=0
d)
5x-4y+1=0
|
|
Nisha Choudhury answered |
Since the point P(x,y) lies on the line joining A(3,4) and B(-5,-6),
Therefore, points P, A and B are collinear points.
So, area of triangle PAB = 0
Therefore, we have:
10x-18-3y-5y+20=0
10x-8y+2=0
5x-4y+1=0 , which is the required condition.
If the four points (0,-1), (6,7),(-2,3) and (8,3) are the vertices of a rectangle, then its area is- a)40 sq. units
- b)12 sq. units
- c)10 sq. units
- d)13 sq. units
Correct answer is option 'A'. Can you explain this answer?
If the four points (0,-1), (6,7),(-2,3) and (8,3) are the vertices of a rectangle, then its area is
a)
40 sq. units
b)
12 sq. units
c)
10 sq. units
d)
13 sq. units
|
|
Arun Sharma answered |
Let A(0-1), B(6,7), C(-2,3) and D(8,3) be the given points. Then
∴ AD = BC and AC = BD
So, ADBC is a parallelogram
Now 
Clearly, AB2 = AD2 + DB2 and CD2 = CB2 + BD2
Hence, ADBC is a rectangle.
Now
,Area of rectangle ADBC = AD × DB =(4√5 × 2√5)sq. units = 40sq. units
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Mid-point of a line segment divides line in the ratio 1 : 1.Reason : If area of triangle is zero that means points are collinear.- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'B'. Can you explain this answer?
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : Mid-point of a line segment divides line in the ratio 1 : 1.
Reason : If area of triangle is zero that means points are collinear.
a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true but R is NOT the correct explanation of A
c)
A is true but R is false
d)
A is false and R is True
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Ishan Choudhury answered |
Let us assume that point B divides the line AC in the ratio k : 1
Let(x1, y1, z1) = (0, 0, 0)
(x, y ,z) = (2, −3, 3)
(x2, y2, z2) = (−2, 3, −3)
By section formula:
x = m1 + m2 m1 x 2 + m2 x 1
⇒ 2 = k + 1 k.(−2) + 1.(0)
⇒ k = 4 − 1 on neglecting the negative sign
we get, therefore ratio is 1:4.
The distance between points (a + b, b + c) and (a – b, c – b) is :- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
The distance between points (a + b, b + c) and (a – b, c – b) is :
a)
b)
c)
d)
|
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Ishan Choudhury answered |
Distance between two point is
root[{(a+b)-(a-b)}^2] + [{(b+c)-(c-b)}^2]
=root [{(a+b-a+b)^2}] + [((b+c-c+b)}^2]
=root[(2b)^2 + (2b)^2]
=root[4b^2 +4b^2]
=root[8b^2]
=2.root(2)b
The co-ordinates of the points which divides the join of (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is :- a)(4, – 4)
- b)(– 3, 1)
- c)(– 4, 4)
- d)(1, – 3).
Correct answer is option 'C'. Can you explain this answer?
The co-ordinates of the points which divides the join of (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is :
a)
(4, – 4)
b)
(– 3, 1)
c)
(– 4, 4)
d)
(1, – 3).
|
|
Kamna Science Academy answered |
To find the co-ordinates that divide the line segment joining the points (–2, –2) and (–5, 7) in the ratio 2:1, use the section formula:
- Let the points be:
- x1 = –2, y1 = –2
- x2 = –5, y2 = 7
- Using the section formula, the co-ordinates are calculated as follows:
- x = (m2x1 + m1x2) / (m1 + m2)
- y = (m2y1 + m1y2) / (m1 + m2)
- Here, m1 = 2 and m2 = 1.
- Substituting the values:
- x = (1 × (–2) + 2 × (–5)) / (2 + 1) = (–2 – 10) / 3 = –4
- y = (1 × (–2) + 2 × 7) / (2 + 1) = (–2 + 14) / 3 = 4
- The result is the point (–4, 4).
If two vertices of a parallelogram are (3, 2) and (–1, 0) and the diagonals intersect at (2, –5), then the other two vertices are :- a)(1, –10), (5, –12)
- b)(1, –12), (5, –10)
- c)(2, –10), (5, –12)
- d)(1, – 10), (2, – 12)
Correct answer is option 'B'. Can you explain this answer?
If two vertices of a parallelogram are (3, 2) and (–1, 0) and the diagonals intersect at (2, –5), then the other two vertices are :
a)
(1, –10), (5, –12)
b)
(1, –12), (5, –10)
c)
(2, –10), (5, –12)
d)
(1, – 10), (2, – 12)
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Parth Chawla answered |
Let's call the two given vertices A and B, with coordinates (3, 2) and (x, y) respectively.
Since a parallelogram has opposite sides that are parallel, we can find the coordinates of the other two vertices by applying the same translation to points A and B.
To find the translation, we can subtract the x-coordinate of point A from the x-coordinate of point B, and subtract the y-coordinate of point A from the y-coordinate of point B:
x - 3 = 3 - 3 = 0
y - 2 = 2 - 2 = 0
So the translation is (0, 0).
To find the coordinates of the other two vertices, we can add the translation to points A and B:
Point A + translation = (3, 2) + (0, 0) = (3, 2)
Point B + translation = (x, y) + (0, 0) = (x, y)
Therefore, the other two vertices of the parallelogram are (3, 2) and (x, y).
Since a parallelogram has opposite sides that are parallel, we can find the coordinates of the other two vertices by applying the same translation to points A and B.
To find the translation, we can subtract the x-coordinate of point A from the x-coordinate of point B, and subtract the y-coordinate of point A from the y-coordinate of point B:
x - 3 = 3 - 3 = 0
y - 2 = 2 - 2 = 0
So the translation is (0, 0).
To find the coordinates of the other two vertices, we can add the translation to points A and B:
Point A + translation = (3, 2) + (0, 0) = (3, 2)
Point B + translation = (x, y) + (0, 0) = (x, y)
Therefore, the other two vertices of the parallelogram are (3, 2) and (x, y).
If (3, 2), (4, k) and (5, 3) are collinear then k is equal to :- a)3/2
- b)2/5
- c)5/2
- d)3/5
Correct answer is option 'C'. Can you explain this answer?
If (3, 2), (4, k) and (5, 3) are collinear then k is equal to :
a)
3/2
b)
2/5
c)
5/2
d)
3/5
|
|
Swara sharma answered |
To determine the value of k, we need to check if the three given points (3, 2), (4, k), and (5, 3) are collinear. Two points are collinear if the slope between them is the same as the slope between any other two points on the line.
Calculating the slope between (3, 2) and (4, k):
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (3, 2) and (4, k), we have:
m = (k - 2) / (4 - 3)
m = (k - 2) / 1
m = k - 2
Calculating the slope between (4, k) and (5, 3):
Using the coordinates (4, k) and (5, 3), we have:
m = (3 - k) / (5 - 4)
m = (3 - k) / 1
m = 3 - k
Since the two slopes are equal, we can equate them:
k - 2 = 3 - k
Solving this equation for k:
2k = 5
k = 5/2
Therefore, the value of k is 5/2, which corresponds to option C.
Calculating the slope between (3, 2) and (4, k):
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (3, 2) and (4, k), we have:
m = (k - 2) / (4 - 3)
m = (k - 2) / 1
m = k - 2
Calculating the slope between (4, k) and (5, 3):
Using the coordinates (4, k) and (5, 3), we have:
m = (3 - k) / (5 - 4)
m = (3 - k) / 1
m = 3 - k
Since the two slopes are equal, we can equate them:
k - 2 = 3 - k
Solving this equation for k:
2k = 5
k = 5/2
Therefore, the value of k is 5/2, which corresponds to option C.
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