Final answer:
To determine if a quadrilateral is a parallelogram, we need to check if opposite sides are parallel and if opposite angles are congruent. The slopes of the lines connecting the given points are equal, indicating that the quadrilateral is a parallelogram.
Step-by-step explanation:
To determine if a quadrilateral is a parallelogram, we need to check if opposite sides are parallel and if opposite angles are congruent. Let's find the slopes of the lines connecting the given points.
The slope between L(-2,3) and M(4,3) is (3-3)/(4-(-2)) = 0.
The slope between N(2,-2) and O(-4,-2) is (-2-(-2))/(-4-2) = 0.
Since the slopes of the opposite sides are equal, the quadrilateral is a parallelogram.