XYWZ is a quadrilateral with vertices W (1, - 4), X (-4, 2), Y (1, - 1), and Z (-2, - 3). Determine if the quadrilateral is a parallelogram. Use slope to justify your answer.

No, the quadrilateral XYWZ is not a parallelogram.

Step-by-step explanation:

Given vertices of a quadrilateral are W (1, - 4), X (-4, 2), Y (1, - 1), and Z (-2, - 3).

Slope formula = (y₂ - y₁) / (x₂ - x₁)

Slope of XY = [-1 - (-2) ]/[1 - (-4) ] = 1/5

Slope of YW = [-1 - (-4) ]/[1 - 1] = 3/0 = Not defined

Slope of WZ = [-3 - (-4) ]/[-2 - 1] = - 1/3

Slope of ZX = [-4 - (-2) ]/[-2 - (-3) ] = - 1/2

⇒XY ∦ WZ and YW ∦ ZX.

Since both sides of opposite sides are not parallal.

Quadrilateral XYWZ is not a parallelogram.