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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