Page 1: (MC 02.03) What set of reflections and rotations would carry rectangle ABCD onto itself? (4 points) 1) Rotat

Question

Page 1:
(MC 02.03)
What set of reflections and rotations would carry rectangle ABCD onto itself?
(4 points)
1) Rotate 180°, reflect over the x-axis, reflect over the line yox
2) Reflect over the x-axis, rotate 180°, reflect over the x-axis
3) Rotate 180°, reflect over the y-axis, reflect over the line y=x
4) Reflect over the y-axis, reflect over the x-axis, rotate 180°

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Peyton 1 week 2021-09-10T12:40:49+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T12:42:03+00:00

    Answer:

    i think it would be number 3.

    Hope this helps.

    Step-by-step explanation:

    0
    2021-09-10T12:42:20+00:00

    Answer:

    4) Reflect over the y-axis, reflect over the x-axis, rotate 180°

    Step-by-step explanation:

    Since, the rule of 180° rotation,

    (x,y)\rightarrow (-x,-y)

    Rule of reflection over x-axis,

    (x,y)\rightarrow (x,-y)

    Rule of reflection over y-axis,

    (x,y)\rightarrow (-x,y)

    Rule of reflection over line y = x,

    (x,y)\rightarrow (y,x)

    ∵ In the set of reflection,

    Rotate 180°, reflect over the x-axis, reflect over the line y=x,

    (x,y)\rightarrow (-x,-y)\rightarrow (-x,y)\rightarrow (y,-x)

    Reflect over the x-axis, rotate 180°, reflect over the x-axis,

    (x,y)\rightarrow (x,-y)\rightarrow (-x,y)\rightarrow (-x,-y)

    Rotate 180°, reflect over the y-axis, reflect over the line y=x,

    (x,y)\rightarrow (-x,-y)\rightarrow (x,-y)\rightarrow (-y,x)

    Reflect over the y-axis, reflect over the x-axis, rotate 180°,

    (x,y)\rightarrow (-x,y)\rightarrow (-x,-y)\rightarrow (x,y)

    Hence, the set of reflections and rotations that would carry rectangle ABCD onto itself is,

    Reflect over the y-axis, reflect over the x-axis, rotate 180°.

    Option ‘4’ is correct.

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