Coordinate Geometry

QUESTION 1
Find the coordinate of the point A , where AB is diameter of a circle whose center is (2, -3) and B is the point (1,4).


QUESTION 2
Find the coordinate of a point A, where AB is diameter of the circle (-2, 2) and B is point with  coordinate (3, 4).

QUESTION 3
Find the ratio in which the segment joining the points (1, -3) and (4, 5) is divided by x-axis? Also find the coordinate of this point on x-axis.

QUESTION 4
Write coordinates of a point P on x-axis which is equidistant from the point A (-2, 0) and B(6, 0).

QUESTION 5
Find the point on y-axis which is equidistant from the point  (5,  -8) and (-3, 2).

QUESTION 6
The line segment joining the point  A(2, 1) and (5, -8) is triscted at the point P and Q sch that P is nearer to A. If P also lies on the line given 2x -y + = 0, find the value of k.


QUESTION 7
Find the distance of a point P (x, y) from the origin.

QUESTION 8
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3) Hence find m.

QUESTION 9
If A(-2,1), B(a, 0), C(4, b) and D(1,2) are the vertices of a parallelogram ABCD, find the values a and  b. Hence find the lengths of its sides.

QUESTION 10
If A(-5, 7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a quadrilateral, find the area of a equilateral ABCD.

QUESTION 11
A(5, 1), B(1, 5) and C(-3, -1) are the vertices of triangle ABC. Find  the length of meridian AD.

QUESTION 12
Find the linear relation between x and y such that P(x, y) is equidistant from from the points A(1, 4) and B(-1, 2).

QUESTION 13
If coordinates of two adjacent vertices of a paralleogram are (3, 2), (1, 0) and diagonal bisect each other at (2, -5), find coordinates of the other two vertices.

QUESTION 14
If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units, find x.

QUESTION 15
If the distance between the point (4, k) and (1, 0) is 5, then what can be the posible values of k.

QUESTION 16
A line intersects the y-axis and x-axis at points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q.

QUESTION 17
If the distance of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.

QUESTION 18
(If two adjacent vertices of a parellogram are (3, 2) and (-1, 0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.

QUESTION 19
Show that triangle ABC, where A(-2, 0), B(2, 0), C(0, 2) and triangle PQR where P(-4, 0), Q(4, 0), R(0, 4) are similar triangles.

QUESTION 20
The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is (7/2, y), find the value of y.