Quadrilateral EFGH has vertices at E(–6,–4), F(–5,4), G(3,3), and H(4,–5).Is EFGH a parallelogram? Justify your answer.

To determine if quadrilateral EFGH is a parallelogram, we need to check if both pairs of opposite sides are equal.

The formula to calculate the distance between two points (x1, y1) and (x2, y2) is √[(x2 - x1)² + (y2 - y1)²].

Let's calculate the lengths of the sides:

EF = √[(-5 - -6)² + (4 - -4)²] = √[1² + 8²] = √65 FG = √[(3 - -5)² + (3 - 4)²] = √[8² + -1²] = √65 GH = √[(4 - 3)² + (-5 - 3)²] = √[1² + -8²] = √65 HE = √[(-6 - 4)² + (-4 - -5)²] = √[-10² + 1²] = √65

Since EF = FG = GH = HE, EFGH is a parallelogram because both pairs of opposite sides are equal.