Question

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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°

Answer 1

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

Explanation:

Answer 2

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

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.