Question

The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.

Answer 1

Let A (3, 4), B (3, 8) and C (9, 8) be the given points.

And let the fourth vertex be D(x, y)

We know that,

In a parallelogram the diagonal bisect each other.

So, the mid-point of AC should be the same as the mid-point of BC

By mid-point theorem,

Mid-point of AC = (3 + 9/ 2), (4 + 8/ 2) = (6, 6)

Now,

The mid-point of BD = (3 + x/ 2, 8 + y/ 2)

And this point must be equal to (6, 6)

So, we have

(3 + x)/ 2 = 6; (8 + y)/ 2 = 6

3 + x = 12: 8; + y = 12

x = 9; y = 4

Therefore, the fourth vertex is D (9, 4)