# 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.

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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