Question

I will prove that quadrilateral MNOP is a rectangle by demonstrating that _. the vertices are M (−6,6), N (−8, −8), O (−1, −9), and P (1,5)

Answer 1

I will prove that quadrilateral MNOP is a rectangle by demonstrating that MN ∥ OP, NO ∥ MP, and MN ⟂ NO.

Compute slopes:
- slope MN = (−8 − 6)/(−8 − (−6)) = −14/−2 = 7
- slope NO = (−9 − (−8))/(−1 − (−8)) = −1/7
- slope OP = (5 − (−9))/(1 − (−1)) = 14/2 = 7
- slope MP = (5 − 6)/(1 − (−6)) = −1/7

Thus MN and OP both have slope 7 (so MN ∥ OP), NO and MP both have slope −1/7 (so NO ∥ MP), and 7·(−1/7) = −1 (so MN ⟂ NO). A parallelogram with a right angle is a rectangle, so MNOP is a rectangle.