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14 March, 06:42

Quadrilateral QRST, with vertices Q (1, 2), R (3, 4), S (5, 6), and T (2, 7), is dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of quadrilateral Q′R′S′T′?

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  1. 14 March, 08:20
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    Step-by-step explanation:

    Given

    Quadrilateral QRST

    Q (1, 2), R (3, 4), S (5, 6), and T (2, 7)

    Dlated Factor = 2

    Required

    Coordinates of quadrilateral Q′R′S′T′

    Provided that a quadrilateral is dilated with the center of dilation at the origin; the new dilated shape is simply the multiplication of the dilation factor by the coordinates of the original shape;

    In other words,

    Q'R'S'T' = Dilation factor * QRST

    When Q = (1,2)

    Q' = 2 * (1,2)

    Q' = (2,4)

    When R = (3,4)

    R' = 2 * (3,4)

    R' = (6,8)

    When S = (5,6)

    S' = 2 * (5,6)

    S' = (10,12)

    When T = (2,7)

    T' = 2 * (2,7)

    T' = (4,14)

    Hence, the coordinates of Q'R'S'T' is

    Q' = (2,4); R' = (6,8); S' = (10,12); T' = (4,14)
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