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(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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slicergiza slicergiza · Answer 1 · 2019-08-16T11:48:01+02:00

Answer:

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

Step-by-step explanation:

Since, the rule of 180° rotation,

[tex](x,y)\rightarrow (-x,-y)[/tex]

Rule of reflection over x-axis,

[tex](x,y)\rightarrow (x,-y)[/tex]

Rule of reflection over y-axis,

[tex](x,y)\rightarrow (-x,y)[/tex]

Rule of reflection over line y = x,

[tex](x,y)\rightarrow (y,x)[/tex]

∵ In the set of reflection,

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

[tex](x,y)\rightarrow (-x,-y)\rightarrow (-x,y)\rightarrow (y,-x)[/tex]

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

[tex](x,y)\rightarrow (x,-y)\rightarrow (-x,y)\rightarrow (-x,-y)[/tex]

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

[tex](x,y)\rightarrow (-x,-y)\rightarrow (x,-y)\rightarrow (-y,x)[/tex]

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

[tex](x,y)\rightarrow (-x,y)\rightarrow (-x,-y)\rightarrow (x,y)[/tex]

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.