Answer:
(D) LP⊥PN
Step-by-step explanation:
A rectangle is a parallelogram with four right angles., thus in order to prove that LMNP is rectangle, we have to show that LP is perpendicular to PN.
The coordinates of vertices are L(-4,1), P(-3,-1) and N(3,2), then
⇒
And,
⇒
Now, taking the dot product, we have
⇒
Since the dot product of two vectors is equal to zero, these vectors are perpendicular.
Also, It is given that LMNP is a parallelogram , therefore
and
Thus, all the angles of the given parallelogram are equal and are equal to 90°, therefore LMNP is a rectangle.
Hence proved.
Thus, option D is correct.