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 midpoint 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 coordinates 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 coordinates 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.
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