Show that A (-4, -7),B (-1, 2), C (8, 5) and D (5, -4) are the vertices of a parallelogram.

In a parallelogram, opposite sides are equal and parallel.

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
.....(1)

Slope m of a line passing through two points A(a,b) and B(c,d) ig given by

In the question,

AB = =

BC = =

CD = =

AD = =

Slope of AB =

Slope of BC =

Slope of CD =

Slope of AD =

As AB = DC and BC = AD

And Slope AB = Slope CD

Slope BC = slope AD

Hence the given points form a parallelogram.