Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle?

Question

Shape ABCD is shown. Point A is at 5, 5. Point B is at 7, 3. Point C is at 3, 0. Point D is at 1, 2.

Prove that segments AD and AB are congruent and parallel
Prove that opposite sides are congruent and that the slopes of consecutive sides are equal
Prove that segments BC and CD are congruent and parallel
Prove that opposite sides are congruent and the slopes of consecutive sides are opposite reciprocals

Answer 1

To prove that quadrilateral ABCD is a rectangle using coordinate geometry, you should demonstrate that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals.

A rectangle has the following properties:

1. Opposite sides are congruent.
2. The slopes of consecutive sides must be opposite reciprocals (meaning they are perpendicular).

Thus, the correct statement to use in this case is:

"Prove that opposite sides are congruent and the slopes of consecutive sides are opposite reciprocals."

This will confirm that quadrilateral ABCD has the necessary properties of being a rectangle.