**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:**

**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:**

**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:**

**Question 4.**

Prove that the points (3,0), (6,4) and (-1,3) are the vertices of a right angled isosceles triangle.

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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 x^{2} + y^{2}.

**Solution:**

**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:**

**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:**

**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

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 20.**

Show that the points (a,a), (-a,-a) and (-√3a, √3 a) are the vertices of an equilateral triangle.

**Solution:**

**Question 21.**

For what values of k are the points (8,1), (3, -2k) and (k, -5) collinear?

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 37.**

If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k.

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 54.**

Show that the points (-2,3) (8,3) and (6, 7) are the vertices of a right triangle.

**Solution:**

**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:**

**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:**

**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:**

**Question 58.**

Find that value of k for which the point (0, 2) is equidistant from two points (3, k) and (k, 5).

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 64.**

Find the value of x for which the points (x – 1), (2,1) and (4,5) are collinear

**Solution:**

**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:**

**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:**

**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:**

**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:**

.

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 74.**

Find the ratio in which the line segment joining the points (1,-3) and (4,5) is divided by x-axis.

**Solution:**

**Short Answer Type Questions II [3 Marks]**

**Question 75.**

** I**f 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:**

**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:**

**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:**

**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:**

**Question 79.**

If the points A(x, y), B(3, 6) and C(-3,4) are collinear, show that x – 3y + 15 = 0.

**Solution:**

**Question 80.**

Find the value of£, for which the points A(6, -1), B(& – 6) and C(0, -7) are collinear.

**Solution:**

**Question 81.**

Find the value ofp, if the points A(l, 2), B(3,p) and C(5, -4) are collinear.

**Solution:**

**Question 82.**

Find the area of the triangle whose vertices are (-7, -3), (1, -7) and (3,0).

**Solution:**

**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:**

>

**Question 84.**

Find the value of y for which the points (5, -4), (3, -1) and (1, y) are collinear.

**Solution:**

**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:**

**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:**

**Question 87.**

Find the point ony-axis which is equidistant from the points (-5, -2) and (3, 2).

**Solution:**

**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:**

**Question 89.**

Find the value of k, if the points P(5,4), Q(7, k) and R(9, -2) are collinear

**Solution:**

**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:**

**Question 91.**

If two vertices of an equilateral triangle are (3,0) and (6,0), find the third vertex.

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 99.**

Find a point on x-axis which is equidistant from A(4, -3) and B(0,11).

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 105.**

If A(l, 2), B(4, 3) and €(6,6) are three vertices of parallelogram ABCD, find co-ordinates of D.

**Solution:**

**Question 106.**

What is the distance between the points A(c, 0) and B(0, -c)?

**Solution:**

**Question 107.**

Find the distance between the points, A(2a, 6a) and B(2a + √3 a, 5a).

**Solution:**

**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:**

**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:**

**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:**

**Question 111.**

Prove that the points P(a, b + c), Q(b, c + a) and R(c, a + b) are collinear.

**Solution:**

**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:**

**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:**

**Question 114.**

Find the value of k, if the points A(7, -2), B(5,1) and C(3,2k) are collinear

**Solution:**

**Question 115.**

If the points (p, q); (m, n) and (p-m,q-n) are collinear, show that pn = qm

**Solution:**

**Question 116.**

Find the value of k, if the points A(8,1), B(3, -4) and C(2, k) are collinear

**Solution:**

**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:**

**Question 118.**

Find the value of k for which the points A(9, k), B(4, -2) and C(3, -3) are collinear.

**Solution:**

**Question 119.**

Find the value of k for which the points A(fc, 5), B(0,1) and C(2, -3) are collinear.

**Solution:**

**Question 120.**

Find the value of p for which the points A(-1, 3), B(2,p) and C(5, -1) are collinear.

**Solution:**