Show that the points A(3,1), B(0, – 2), C(1, 1) and D(4, 4) are the vertices of a parallelogram ABCD.

Question

Philoid · Accepted Answer

We know that the diagonals of a parallelogram bisect each other

So the coordinates of the mid – point of the AC = Coordinates of the mid – point of the BD

Coordinates of mid – point of AC

{(3 + 1)/2,(1 + 1)/2} = (2,1)

Coordinates ofmid – point of BD

{(0 + 4)/2,(– 2 + 4)/2} = (2,1)

Hence, ABCD is a parallelogram.