Question

A (−2, 2), B(8, 2) and C(4, −4) are the vertices of a parallelogram ABCD. By plotting the given points on a graph paper, find the coordinates of the fourth vertex D.

Also, form the same graph, state the co-ordinates of the mid-points of the sides AB and CD.

Answer 1

Plot the points A, B, and C on the graph paper. Join the points to complete the parallelogram ABCD. As the distance between points A and B is 10 units, distance between the corners of the opposite side C and D will also be 10 units.

Hence, the fourth point D = (−6, −4)

Mid point of AB will lie at 5 units distance from A and B both which is = (3, 2)

Mid point of CD will lie at 5 units distance from C and D both which is = (−1, −4)