Question

Prove that the quadrilateral whose vertices are A(-2, 5), B(4, -1), C(9, 1) and D(3, 7) is a parallelogram and find its area. If E divides AC in the ratio 2:1, prove that D, E and the middle point F of BC are collinear.

Answer 1

Given: Let ABCD is a quadrilateral whose vertices A(-2, 5), B(4, -1), C(9, 1) and D(3, 7).

To prove: ABCD is a parallelogram .

We have to find |AD|, |AB|, |BC|, |DC|

The distance between two sides

Therefore, AB = DC and AD = BC

Hence, ABCD is a parallelogram

Now, The Area of ABCD is = |a × b|

= 0i – 0j+ 42 k

|a×b| = 42

Hence The area of parallelgram is 42