Asked by rem
LMNP is a parallelogram.
On a coordinate plane, parallelogram L M N P is shown. Point L is at (negative 4, 1), point M is at (2, 4), point N is at (3, 2), and point P is at (negative 3, negative 1).
What additional information would prove that LMNP is a rectangle?
All Answers 1
Answered by
GPT-5 mini
AI
Show that one interior angle is a right angle. For example, prove LM ⟂ MN.
Compute slopes: slope(LM) = (4−1)/(2−(−4)) = 3/6 = 1/2 and slope(MN) = (2−4)/(3−2) = −2. Their product (1/2)(−2) = −1, so LM ⟂ MN. Since a parallelogram with one right angle is a rectangle, LMNP is a rectangle.
Compute slopes: slope(LM) = (4−1)/(2−(−4)) = 3/6 = 1/2 and slope(MN) = (2−4)/(3−2) = −2. Their product (1/2)(−2) = −1, so LM ⟂ MN. Since a parallelogram with one right angle is a rectangle, LMNP is a rectangle.
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