Question

Prove that the quadrilateral with the coordinates L(-2,3), M(4,3), N(2,-2) and O(-4,-2) is a parallelogram.

Answer 1

ANSWER

LMNO is a parallelogram

EXPLANATION

Segments LM and NO are parallel, because they are both horizontal lines. Also, they are congruent because the horizontal distance between the endpoints is the same for both segments:

$\begin{gathered} d_{LM}=|-2-4|=|-6|=6 \\ d_{NO}=|2-(-4)|=|2+4|=6 \end{gathered}$

Then, segments LO and NM are parallel too. We can prove this with the slope

The slope is:

$\text{slope}=\frac{\text{rise}}{\text{run}}$

For both segments, the rise is 5 - which is the height of the parallelogram - and the run is 2. Therefore they have the same slope, so they are parallel.

Hence, LMNO is a parallelogram.