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

Question

The vertices of JOHN are J(­3,1), O(3,3), H(5,7) and N(­1,5). Use

coordinate geometry to prove that Quadrilateral JOHN is a parallelogram.

Answer 1

JO is a vertical line, undefined slope 2/0, length 3-1 = 2

OH has slope 2, length sqr20

HN has slope 1/2, length sqr20

NJ has slope-2, length sqr20

to be a parallelogram, opposite sides must be parallel, i.e. have the same slope

every side of this quadrilateral has a different slope. No sides are parallel. It's not a parallelogram