The vertices of quadrilateral JOHN are J(-3, 1), O(3, 3), H(5, 7), and N(-1, 5). Use co- ordinate geometry to prove that quadrilateral JOHN is a parallelogram.

Question

The vertices of quadrilateral JOHN are J(-3, 1), O(3, 3), H(5, 7), and N(-1, 5). Use co- ordinate geometry to prove that quadrilateral JOHN is a parallelogram.

Answer 1

Compute the slopes of all 4 sides of the parallelogram:

lines between coordinates of::

JO

OH

HN

NJ

If slopes of lines between opposite sides JO and HN are equal then they are parallel

If slopes of lines between opposites OH and NH are equal then they are parallel

If both pairs of opposite sides are parallel, then by definition JOHN is a parallelogram.