Question Bank: COORDINATE GEOMETRY
1) If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then find the
value of x?
2) The points A(-6, -5); B(1,-5); C(p,0) and D(-4,0) are the vertices of a parallelogram
ABCD. Find the value of p.
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3) P( , 4) is a midpoint of the line segment QR such that Q(6,5) and R(2,3). Find the
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value of a.
4) Three consecutive vertices of a parallelogram ABCD are A(1, -2) B(3,6) C(5,10). Find
the coordinates of vertex D.
5) Points A(-1, y) and B(5,7) lie on a circle with centre O(2,-3y). Find the value of y.
6) If the distance between A(2,3), B(k,1) is 2√2 units. Find k.
7) If A(-1,2) B(2,-1) C(3,1) and D(a,b) are the vertices of a parallelogram ABCD, find the
coordinates of a, b of vertex D.
8) Find the coordinates of point P which divides the line of (-2,2) and (-5,7) in the ratio
of 2:1.
9) Find the coordinates of the point P(x,y) which divides the line segment AB joining the
two points, A(4, -3) and B(9,7) in the ratio 3:2.
10) If Q(0,1) is equidistant from P(5,-5) and R(x,6), find the value of x.
11) If A(3,3) B(6,y) C(x,7) and D(5,6) are the vertices of a parallelogram ABCD, find the
value of x and y.
12) Find the ratio in which the y-axis divides the line segment joining the points A(4,3)
and B(-3,4) and also write the coordinates of the point on the y-axis.
13) If A(1,2) B(4,y) C(x,6) and D(3,5) are the vertices of parallelogram ABCD, find the
value of x and y.
14) Find the distance between the points P(5,2) and Q(-3, -4).
15) Find the value of y for which the distance between the points P(2, -3) and Q(10, y) is
10 units.
16) Find the coordinates of the points on the x-axis which are at a distance of 5 units
from the point (6, -3).
17) The mid points of sides PQ and PR of triangle PQR are S(-4, 7) and T(2, -1)
respectively. Find the length of side QR.
18) If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that
7AP=3AB and P lies on the line segment AB.
19) Find the coordinates of the point of trisection of the line segment joining the points
P(4, -1) and Q(-2, -3).
20) A point P(x,y) divides the segment joining the points (-1, -2) and (4, -7) in the ratio
2:3. Find the values of x and y.
21) Find the relationship between x and y such that the point P(x,y) is equidistant from
the points A(3,7) and B(2,2).
22) If a line segment joining P(-5, -3) and Q(1, 3) intersects the X-axis at its midpoint, find
the coordinates of the midpoint.
1) If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then find the
value of x?
2) The points A(-6, -5); B(1,-5); C(p,0) and D(-4,0) are the vertices of a parallelogram
ABCD. Find the value of p.
𝑎
3) P( , 4) is a midpoint of the line segment QR such that Q(6,5) and R(2,3). Find the
3
value of a.
4) Three consecutive vertices of a parallelogram ABCD are A(1, -2) B(3,6) C(5,10). Find
the coordinates of vertex D.
5) Points A(-1, y) and B(5,7) lie on a circle with centre O(2,-3y). Find the value of y.
6) If the distance between A(2,3), B(k,1) is 2√2 units. Find k.
7) If A(-1,2) B(2,-1) C(3,1) and D(a,b) are the vertices of a parallelogram ABCD, find the
coordinates of a, b of vertex D.
8) Find the coordinates of point P which divides the line of (-2,2) and (-5,7) in the ratio
of 2:1.
9) Find the coordinates of the point P(x,y) which divides the line segment AB joining the
two points, A(4, -3) and B(9,7) in the ratio 3:2.
10) If Q(0,1) is equidistant from P(5,-5) and R(x,6), find the value of x.
11) If A(3,3) B(6,y) C(x,7) and D(5,6) are the vertices of a parallelogram ABCD, find the
value of x and y.
12) Find the ratio in which the y-axis divides the line segment joining the points A(4,3)
and B(-3,4) and also write the coordinates of the point on the y-axis.
13) If A(1,2) B(4,y) C(x,6) and D(3,5) are the vertices of parallelogram ABCD, find the
value of x and y.
14) Find the distance between the points P(5,2) and Q(-3, -4).
15) Find the value of y for which the distance between the points P(2, -3) and Q(10, y) is
10 units.
16) Find the coordinates of the points on the x-axis which are at a distance of 5 units
from the point (6, -3).
17) The mid points of sides PQ and PR of triangle PQR are S(-4, 7) and T(2, -1)
respectively. Find the length of side QR.
18) If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that
7AP=3AB and P lies on the line segment AB.
19) Find the coordinates of the point of trisection of the line segment joining the points
P(4, -1) and Q(-2, -3).
20) A point P(x,y) divides the segment joining the points (-1, -2) and (4, -7) in the ratio
2:3. Find the values of x and y.
21) Find the relationship between x and y such that the point P(x,y) is equidistant from
the points A(3,7) and B(2,2).
22) If a line segment joining P(-5, -3) and Q(1, 3) intersects the X-axis at its midpoint, find
the coordinates of the midpoint.
