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24 August, 05:45

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.

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  1. 24 August, 06:56
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    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.
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