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.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

the answer is d

step-by-step explanation: