Lmnp is a parallelogram.
what additional information would prove that lmnp is a rectangle?
a. the length of lm is √45 and the length of mn is √5.
b. the slope of lp and mn is –2.
c. lm ∥ pn
d. lp ⊥ pn

A rectangle is a parallelogram with four right angles.

That's why in order to prove that LMNP is rectangle you have to show that LP is perpendicular to PN.

Solution:

The coordinates of vertices are L(-4,1), P(-3,-1) and N(3,2), then

.

Find the dot product:

.

Since the dot product of two vectors is equal to zero, these vectors are perpendicular.

LMNP is a parallelogarm, then

.

You show that all angles are right, this means that parallelogram LMNP is a rectangle.

correct choice is D.

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: