Question

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

Explanation:

Step1: Recall rectangle properties

A parallelogram is a rectangle if adjacent sides are perpendicular.

Step2: Check adjacent sides' slopes

For LP: slope = (-1-1)/(-3-(-4)) = -2/1 = -2. For PN: slope = (2-(-1))/(3-(-3)) = 3/6 = 1/2.

Step3: Perpendicularity condition

Product of slopes: (-2)(1/2) = -1, so LP ⊥ PN implies right angle.

Answer:

LP ⊥ PN