Q. 74.0( 25 Votes )

Prove that the point (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are the corners of a parallelogram. And find its area.

Answer :

let A = (-7,-3) B = (5,10) and C = (15,8) D = (3,-5)

Let these points be a parallelogram.


So midpoints of AC and DB should be same.


To find midpoint of AC and DB



For AC =


AC =


AC =


For DB


DB =


DB =


DB =


As midpoints of AC and DB are same the points form a parallelogram.


Let us divide the parallelogram into 2 triangle ΔABD and ΔBCD


Area of both triangles


Area ΔABD =


=


=


=


=


= 77


Area ΔBCD =


=


=


=


= 77


Total area of parallelogram = Sum of Area of triangles


= ΔBCD + ΔABD


= 154 units


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