Question

if the points (-2 -1) , (1 0) , (x 3) , (3 y) form a parallelogram, find the values of x and y.

Answer 1

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Let the vertices of the parallelogram be A(-2, -1), B(1, 0), C(x, 3) and D(1, y). Since the diagonals of a parallelogram bisect each other the coordinates of the mid-point of AC = coordinates of the mid-point of BD.

(-2+x/2 , -1+3/2) = (3+1/2 , 0+y/2)

(-2+x/2, 1) = (2,y/2)

∴ x = 6, y = 2