Find the image of O (0,0) after two reflections, first across L1 and then across L2: L1: y = 2 L2: x = -3

Question

Find the image of O (0,0) after two reflections, first across L1 and then across L2: L1: y = 2 L2: x = -3

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    0
    2021-09-06T09:55:24+00:00

    Answer:

    the answer is (-6, -4) (i think)

    Step-by-step explanation:

    the answer for L1 is (0, -4) and the answer for L2 is (-6, 0)

    those two put together is (-6, -4)

    hope this helps 🙂

    0
    2021-09-06T09:55:27+00:00

    Some standard rules:
    S_x(x,y)\rightarrow(x,-y+2k) reflection about horizontal line y=k
    S_y(x,y)\rightarrow(-x+2h,y) reflection about vertical line x=h

    So for O(0,0), h=-3, k=2
    First reflection about L1: y=2
    (x,y)->(x, -y+2(k)) =>
    O(0,0)->O'(0,-0+2(2) = O'(0,4)
    Second reflection about L2: x=-3
    (x,y)->(-x+2h,y) =>
    O'(0,4)->O”(0+2(-3),4) = O”(-6,4)

    Answer: after both reflections, the position of image is O”(-6,4)

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