Q25 of 184 Page 10

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.

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


|AD|


= √29


|AB| =


= √72


|DC| =


= √72


|BC| =


= √29


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


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