Question

LMNP is a parallelogram.

Answer 1

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

$\overrightarrow{PL}=(-4-(-3),1-(-1))=(-1,2),\\ \overrightarrow{PN}=(3-(-3),2-(-1))=(6,3)$.

Find the dot product:

$\overrightarrow{PL}\cdot \overrightarrow{PN}=-1\cdot 6+2\cdot 3=-6+6=0$.

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

LMNP is a parallelogarm, then

$m\angle P=m\angle M=90^{\circ},\\ m\angle L=m\angle N=180^{\circ}-90^{\circ}=90^{\circ}$.

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

Answer: correct choice is D.

Answer 2

Answer:

D

Step-by-step explanation:

EDGE