Question

If two vertices of a parallelogram are (3, 2) (−1, 0) and the diagonals cut at (2, −5), find the other vertices of the parallelogram.

Answer 1

We have a parallelogram ABCD in which A (3, 2) and B (−1, 0) and the co-ordinate of the intersection of diagonals is M (2,−5).

We have to find the co-ordinates of vertices C and D.

So let the co-ordinates be and

In general to find the mid-point of two pointsand we use section formula as,

The mid-point of the diagonals of the parallelogram will coincide.

So,

Therefore,

Now equate the individual terms to get the unknown value. So,

So the co-ordinate of vertex C is (1,−12)

Similarly,

Therefore,

Now equate the individual terms to get the unknown value. So,

So the co-ordinate of vertex C is (5,−10)