ΔABC has coordinates of A (–6, –7), B (4, –2), and C (0, 7). Find the coordinates of its image after a dilation centered at the origin

Question

ΔABC has coordinates of A (–6, –7), B (4, –2), and C (0, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.

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    0
    2021-10-11T05:33:50+00:00

    The rule for dilation (scale factor k) about the origin is given by:
    (x,y)->(kx,ky)
    This means that when k=2,
    (x,y)->(2x,2y) after dilation.
    A(-6,-7)->A'(-12,-14)
    B(4,-2)->B'(8,-4)
    C(0,7)->C'(0,14)

    0
    2021-10-11T05:33:56+00:00

    A dilation with a scale factor k about the origin can be described using the following notation:

    (x,y)→(kx,ky).

    In your case, k=2, then

    • A (–6, –7)→A'(2·(-6),2·(-7))=A'(-12,-14);
    • B (4, –2)→B'(2·4,2·(-2))=B'(8,-4);
    • C (0, 7)→C'(2·0,2·7)=C'(0,14).

    Answer: A'(-12,-14), B'(8,-4), C'(0,14).

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