Question

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.

Answer 1

Explanation:

Answer 2

No, the quadrilateral XYWZ is not a parallelogram.

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.