Question

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?

Answer 1

Answer:

D. LP ⊥ PN

Step-by-step explanation:

A rectangle is a four-angle parallelogram, so to demonstrate that LMNP is a rectangle, we must prove that LP is perpendicular to PN.

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

PL = (-4 + 3, 1 + 1)

PL = (-1 , 2)

And,

PN = (3 + 3, 2 + 1)

PL = (6,3)

Now, consider the dot product,

PL.PN = (-1) (6) + (2) (3)

PL.PN = 0

As we can see that the two vectors having dot product is equal to zero as these vectors considered to be perpendicular.

Plus, It is mentioned that LMNP is a parallelogram

So,

m∠P  = m∠M = 90° and m∠L = m∠N = 180° - 90° = 90°

Therefore all parallelograms angles are equal to each other

Therefore the LMNP is a rectangle