Worksheet: Coordinate Geometry

Multiple choice Questions
Q1: Find the centroid of the triangle XYZ whose vertices are X (3, - 5) Y (- 3, 4) and Z (9, - 2).
(a) (0, 0)
(b) (3, 1)
(c) (2, 3)
(d) (3,-1)

Q2: If the mid-point of the line segment joining the points A (3, 4) and B (a, 4) is P (x, y) and x + y - 20 = 0, then find the value of a
(a) 0
(b) 1
(c) 40
(d) 45

Q3: Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A (2, - 2) and B (3, 7).
(a) 2:9
(b) 1:9
(c)1:2
(d) 2:3

Short Answer type
Q4: The coordinates of one end point of a diameter of a circle are (4, -1) and the co-ordinates of the centre of the circle are (1, -3). Find the co- ordinates of the other end of the diameter.

Q5: If the mid- point of the line joining (3, 4) and (z, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of z.

Long Answer Type
Q6: Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3) 

Q7: Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus. Also, find its area.

Q8: Two opposite vertices of a square are (-1, 2) and (3, 2). Find thee co-ordinates of other two vertices.

Q9: Find a point on y - axis which is equidistant from the points (5, -2) and (-3, 2).

Q10: If the coordinates of the mid points of the sides of a triangle are (1, 2), (0, -1) and (2, -1). Find the coordinates of its vertices.

You can access the solutions to this worksheet here.