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Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions

Important Questions for Class 10 Maths Chapter 7 Coordinate Geometry with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 7 Coordinate Geometry.

Important Questions for Class 10 Maths Chapter 7 Coordinate Geometry

Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 7 Coordinate Geometry.

MathsScienceEnglishSocialHindi AHindi B

2016

Short Answer Type Questions I [2 Marks]

Question 1.
Find the ratio in which y-axis divides the line segment joining the points A(5, -6) and B(-l, -4). Also find the coordinates of the point of division.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 1

Question 2.
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, -5) and R(-3, 6), find the coordinates of P.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 2

Question 3.
Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 3

Question 4.
Prove that the points (3,0), (6,4) and (-1,3) are the vertices of a right angled isosceles triangle.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 4

Question 5.
Find the ratio in which the point (-3, k) divides the line-segment joining the points (-5, -4) and (-2,3). Also find the value of k.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 5

Question 6.
Prove that the points (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Also find the area of this triangle.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 6

Short Answer Type Questions II [3 Marks]

The advanced version of the midpoint calculator helps to find the distance and midpoint between any given points for 1 through 6 dimensions.

Question 7.
In figure ABC is a triangle coordinates of whose vertex A are (0, -1). D and E respectively are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0,1) respectively. If F is the mid-point of BC, find the areas of ∆ABC and ∆DEF.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 7
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 8
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 9

Question 8.
If the point P(x, y) is equidistant from the points A (a + b, b – a) and B(a -b,a+ b). Prove that bx = ay.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 10

Question 9.
If the point C(-l, 2) divides internally the line-segment joining the points A(2, 5) and B(x,y) in the ratio 3 : 4, find the value of  x2 + y2.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 11

Long Answer Type Questions [4 Marks]

Question 10.
Prove that the area of a triangle with vertices (t, t – 2), (t + 2, t + 2) and (t + 3, t) is independent of t.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 12

Question 11.
In fig., the vertices of AABC are A(4, 6), B(l, 5) and C(7, 2). A line-segment DE is drawn to intersect the sides AB and AC
at D and E respectively such that AD/AC=AE/AC=1/3. Calculate the area of ∆ADE and compare it with area of ∆ABC.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 13
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 14

Question 12.
The coordinates of the points A, B and C are (6,3), (-3,5) and (4, -2) respectively.P(JC, y) is any point in the plane. Show that Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 15
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 16

Question 13.
Find the area of the quadrilateral ABCD, the coordinate of whose vertices are A(1, 2), B(6,2), C(5,3) and D(3,4).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 17

Question 14.
Find the area of a quadrilateral ABCD, the coordinates of whose vertices are A(—3,2), B(5,4), C(7, -6) and D(-5, -4).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 18
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 19

2015

Short Answer Type Questions I [2 Marks]

Question 15.
If A(5, 2), B(2, -2) and C(-2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 20

Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 21

Question 16.
Find the ratio in which the point P P(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and 3(2, -5).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 22

Question 17.
The points A(4,7), B(p, 3) and C(7,3) are the vertices of a right triangle, right-angled at B. Find the value of p.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 23

Question 18.
Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 24

Question 19.
If A(4,3), B(-l,y) and C(3,4) are the vertices of right triangle ABC, right-angled at A, then find the value ofy.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 25

Question 20.
Show that the points (a,a), (-a,-a) and (-√3a, √3 a) are the vertices of an equilateral triangle.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 26
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 27

Question 21.
For what values of k are the points (8,1), (3, -2k) and (k, -5) collinear?
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 28

Short Answer Type Questions II [3 Marks]

Question 22.
Find the area of the triangle ABC with A(l, -4) and mid-points of sides through A being (2, -1) and (0, -1).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 29

Question 23.
Find the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1,2).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 30
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 31

Question 24.
If the coordinates of points A and B are (-2, -2) and (2, – 4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 32

Question 25.
Find the coordinates of a point P on the line segment joining A(l, 2) and B(6,7) such that AP=2/5AB
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 33

Question 26.
Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that PA/PQ=2/5. If point P also lies on the line 3x + k(y + 1) = 0, find the value of k
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 34

Long Answer Type Questions [4 Marks]

Question 27.
If A(-4,8), B(-3, -4), C(0, – 5) and D(5,6) are the vertices of a quadrilateral ABCD, find its area.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 35

Question 28.
If P(-5, -3), Q (-4, -6), R(2, -3) and S(l, 2) are the vertices of a quadrilateral PQRS, find its area.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 36

Question 29.
Find the values of k so that the area of the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 37
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 38

Question 30.
Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 39

Question 31.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the mid-point of the base. Find the coordinates of the points A and B. Also find the coordinates of another point D such that BACD is a rhombus.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 40
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 146

2014

Short Answer Type Questions II [3 Marks]

Question 32.
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also find the length of AB.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 41

Question 33.
If the points A(-2,1), B (a, b) and C(4, -1) are collinear and a – b = 1, find the value of a and b.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 42

Question 34.
If the points P(-3,9), Q(a, b) and R(4, -5) are collinear and a + b = 1, find the value of a and b.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 43

Question 35.
Points A(-l, y) and B(5,7) lie on a circle with centre 0(2, -3y). Find the values ofy. Hence, find the radius of the circle.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 44

Question 36.
If the point A(-l, -4); B(b, c) and C(5, -1) are collinear and 2b+ c = 4, find the value of b and c.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 45

Question 37.
If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 46

Question 38.
If the point P(k – 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 47

Question 39.
Find the ratio in which the line segment joining the points A(3, -3) and B(-2, 7) is divided by x-axis. Also find the coordinates of the point of division.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 48
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 49

Question 40.
Prove that the diagonals of a rectangle ABCD, with vertices A(2, – 1), B(5, – 1), C(5,6) and D(2,6), are equal and bisect each other.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 50

Question 41.
Find a point P on they-axis which is equidistant from the points A(4,8) and B(- 6, 6). Also find the distance AP.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 51

Question 42.
Find the value(s) of k for which the points (3k – 1, k – 2), (k, k-1) and (k – 1, – k – 2) are collinear
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 52

Question 43.
points P, Q, R and S divide the line segment joining the points A(l, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 53

Question 44.
Find the value(s) of p for which the points (p + 1, 2p – 2), (p – 1 ,p) and (p -6, 2p – 6) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 54
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 55

Question 45.
Find the value(s) of p for which the points (3p + 1, p), (p + 2, p – 5) and (p + 1, -p) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 56

Long Answer Type Questions [4 Marks]

Question 46.
Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12,5) and B(4, -3). Also, find the value of x.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 57

Question 47.
If A(-3,5), B(-2, -7), C(l, -8) and D(6,3) are the vertices of a quadrilateral ABCD, find its area.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 58

Question 48.
A(4, -6), B(3, -2) and C(5, 2) are the vertices of a AABC and AD is its median. Prove that the median AD divides AABC into two triangles of equal areas.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 59

Question 49.
If A(4,2), B(7,6) and C(l, 4) are the vertices of a ∆ABC and AD is its median, prove that the median AD divides ∆ABC into two triangles of equal areas
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 60

Question 50.
The mid-point P of the line segment joining the points A(- 10, 4) and B(- 2, 0) lies on the line segment joining the points C(- 9, – 4) and D(- 4, y). Find the ratio in which P divides CD. Also find the value of y.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 61

2013

Short Answer Type Questions II [3 Marks]

Question 51.
Prove that the points (7,10), (-2,5) and (3, -4) are the vertices of an isosceles right triangle.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 62

Question 52.
Find, the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10,12). Also find the coordinates of the point of division.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 63

Question 53.
Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 64
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 65

Question 54.
Show that the points (-2,3) (8,3) and (6, 7) are the vertices of a right triangle.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 66

Question 55.
Prove that the points A(2, 3), B(-2, 2), C(-l, -2) and D(3, -1) are the vertices of a square ABCD.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 67
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 68

Question 56.
Find the ratio in which point P(-l, y) lying on the line segment joining points A(-3,10) and B(6, -8) divides it. Also find the value of y.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 69

Question 57.
Prove that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus ABCD. Is ABCD a square?
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 70

Question 58.
Find that value of k for which the point (0, 2) is equidistant from two points (3, k) and (k, 5).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 71

Question 59.
If the point P(x,y) is equidistant from two points A (-3,2) and B (4, -5), prove that y = x- 2.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 72

Question 60.
The line segment AB joining the points A(3, – 4), and B(l, 2) is trisected at the points P(p, – 2) and Q(5/3, q). Find the values of p and q.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 73

Question 61.
If the point A (x, y) is equidistant from two points P (6, -1) and Q (2,3), prove that y = x – 3.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 74
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 75

Question 62.
If the point R (x, y) is equidistant from two points P (- 3, 4) and Q (2, – 1), prove that y = x + 2.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 76

Long Answer Type Questions [4 Marks]

Question 63.
If the area of AABC formed by A(x, y), B(l, 2) and C(2, 1) is 6 square units, then prove that x +y= 15.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 77

Question 64.
Find the value of x for which the points (x – 1), (2,1) and (4,5) are collinear
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 78

Question 65.
The three vertices of a parallelogram ABCD are A(3, -4), B(-l, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of parallelogram ABCD.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 79

Question 66.
If the points A(l, -2), B(2,3), C(-3,2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 80

Question 67.
For the AABC formed by the points A(4, -6), B(3, -2) and C(5,2), verify that median divides the triangle into two triangles of equal area.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 81
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 82
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 83
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 84

Question 68.
Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3,5) and C(2, 6).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 85.

Question 69.
If the area of the triangle formed by points A (x,y), B (1,2) and C (2,1) is 6 square units, then show that x + y = 15.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 86

Question 70.
Find the area of the triangle formed by joining the mid-points of the sides of a triangle whose vertices are (3,2), (5,4) and (3, 6).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 87
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 88

Question 71.
If the area of the triangle formed by joining the points A (x, y), B (3, 2) and C (- 2, 4) is 10 square units, then show that 2x + 5y + 4 = 0.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 89

2010

Very Short Answer Type Questions [1 Mark]

Question 72.
If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find the value of p.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 90

Question 73.
Find the value of k, if the point P(2,4) is equidistant from the points A(5, k) and B(k, 7).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 91

Question 74.
Find the ratio in which the line segment joining the points (1,-3) and (4,5) is divided by x-axis.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 92

Short Answer Type Questions II [3 Marks]

Question 75.
If the vertices of a triangle are (1, – 3) (4,p) and (-9,7) and its area is 15 sq. units, find the value(s) of p.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 93

Question 76.
A point P divides the line segment joining the points A(3, -5) and B(-4, 8) such AP/PB=k/1. If P lies on the line x + y = 0, then find the value of K.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 94
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 95

Question 77.
Find the coordinates of a point P, which lies on the line segment joining the points A(-2, -2) and B(2, -4) such that AP =3/7 AB.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 96

Question 78.
Find the area of the quadrilateral ABCD whose vertices are A(-3, -1), B(-2, -4), C(4, – 1) and D(3, 4).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 97
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 98

Question 79.
If the points A(x, y), B(3, 6) and C(-3,4) are collinear, show that x – 3y + 15 = 0.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 99

Question 80.
Find the value of£, for which the points A(6, -1), B(& – 6) and C(0, -7) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 100

Question 81.
Find the value ofp, if the points A(l, 2), B(3,p) and C(5, -4) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 101

Question 82.
Find the area of the triangle whose vertices are (-7, -3), (1, -7) and (3,0).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 102

Question 83.
Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the coordinates of the point of intersection.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 103
>Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 104

Question 84.
Find the value of y for which the points (5, -4), (3, -1) and (1, y) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 105

Question 85.
For what value of k, (k > 0), is the area of the triangle with vertices (-2, 5), (k, -4) and {2k + 1,10) equal to 53 sq. units?
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 106

2011

Short Answer Type Questions I [2 Marks]

Question 86.
Find that value(s) of x for which the distance between the points P(JC, 4) and Q(9,10) is 10 units.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 107

Question 87.
Find the point ony-axis which is equidistant from the points (-5, -2) and (3, 2).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 108

Question 88. .
If P(2,4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance PQ.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 109

Question 89.
Find the value of k, if the points P(5,4), Q(7, k) and R(9, -2) are collinear
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 110

Question 90.
If (3, 3), (6, y), (x, 7) and (5, 6) are the vertices of a parallelogram taken in order, find the values of x and y.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 111

Question 91.
If two vertices of an equilateral triangle are (3,0) and (6,0), find the third vertex.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 112
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 113

Question 92.
Point M(11,y) lies on the line segment joining the points P(15,5) and Q(9,20). Find the ratio in which point M divides the line segment PQ. Also find the value ofy
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 114

Question 93.
The point A(3,y) is equidistant from the points P(6,5) and Q(0, -3). Find the value of y.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 115

Question 94.
Point P(x, 4) lies on the line segment joining the points A(-5,8) and B(4, -10). Fmd the ratio in which point P divides the line segment AB. Also find the value of x
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 116

Question 95.
Find the area of the quadrilateral ABCD, whose vertices are A(-3, -1), B(-2, -4), C(4, -1) and D(3, 4).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 117

Question 96.
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are A(2,1), B(4,3) and C(2,5).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 118

Question 97.
Find the value of y for which the distance between the points A(3, -1) and B(11,y) is 10 units.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 119

Question 98.
Find a relation between jt and y such that the point P(x, y) is equidistant from the points A(1, 4) and B(-1, 2).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 120

Question 99.
Find a point on x-axis which is equidistant from A(4, -3) and B(0,11).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 121

Question 100.
If A(-2,3), B(6,5), C(x, – 5) and D(-4, – 3) are the vertices of a quadrilateral ABCD of area 80 sq. units, then find positive value of x.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 122

Question 101.
Find the area of the quadrilateral PQRS whose vertices are P(-l, – 3), Q(5, – 7), R(10, — 2) and S(5,17).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 123
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 124

Question 102.
Find the area of the quadrilateral ABCD whose vertices are A(3, – 1), B(9, -5), C(14,0) and D(9,19).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 125

Question 103.
Find the coordinates of the points which divide the line segment joining A (2, – 3) and B(-4, – 6) into three equal parts.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 126

2010

Very Short Answer Type Questions [1 Mark]

Question 104.
If P(2, p) is the mid-point of the line segment joining the points A(6, -5) and B(-2,11), find the value of p.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 127

Question 105.
If A(l, 2), B(4, 3) and €(6,6) are three vertices of parallelogram ABCD, find co-ordinates of D.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 128

Question 106.
What is the distance between the points A(c, 0) and B(0, -c)?
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 129

Question 107.
Find the distance between the points, A(2a, 6a) and B(2a + √3 a, 5a).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 130

Question 108.
Find the value of k if P(4, -2) is the mid point of the line segment joining the points A(5k, 3) and B(-k, —7).
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 131

Short Answer Type Questions II [3 Marks]

Question 109.
Point P divides the line segment joining the points A(2,1) and B(5, -8) such that AP /AB=1/3. If P lies on the line 2x – y + k = 0, find the value of k.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 132

Question 110.
If R(x, y) is a point on the line segment joining the points P(a, b) and Q(b, a), then prove that x + y = a + b.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 133

Question 111.
Prove that the points P(a, b + c), Q(b, c + a) and R(c, a + b) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 134
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 135

Question 112.
If the point P(m, 3) lies on the line segment joining the points A(-2/5,6)  and B(2, 8), find the value of m.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 136

Question 113.
Point P divides the line segment joining the points A(-l, 3) and B(9, 8) such that AP/PB=k/1. If P lies on the line x -y + 2 = 0, find the value of k.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 137

Question 114.
Find the value of k, if the points A(7, -2), B(5,1) and C(3,2k) are collinear
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 138

Question 115.
If the points (p, q); (m, n) and (p-m,q-n) are collinear, show that pn = qm
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 139

Question 116.
Find the value of k, if the points A(8,1), B(3, -4) and C(2, k) are collinear
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 140

Question 117.
If point P (1/2, y )lies on the line segment joining the points A(3, -5) and B(-7,9) then find the ratio in which P divides AB. Also find the value of y.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 141
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 142

Question 118.
Find the value of k for which the points A(9, k), B(4, -2) and C(3, -3) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 143

Question 119.
Find the value of k for which the points A(fc, 5), B(0,1) and C(2, -3) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 144

Question 120.
Find the value of p for which the points A(-1, 3), B(2,p) and C(5, -1) are collinear.
Solution:
Coordinate Geometry Class 10 Maths CBSE Important Questions With Solutions 145

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