Question

What set of reflections and rotations would carry rectangle ABCD onto itself?

A.) reflect over the y-axis, reflect over the x-axis, rotate 180°
B.) rotate 180°, reflect over the x-axis, reflect over the line y=x
C.) reflect over the x-axis, rotate 180°, reflect over the x-axis
D.) rotate 180°, reflect over the y-axis, reflect over the line y=x

Answer 1

Option A is correct.

Explanation:

Rules of Reflection:

Along y-axis

`(x,y)\Rightarrow(-x,y)`

Alon x-axis

`(x,y)\Rightarrow(x,-y)`

The rotation rule: is when any coordinate rotated
`180^(\circ)` the coordinate becomes negation of both k and h.

So, (k,h) becomes (-k,-h)

Let us assume two points (x,y)

When reflected along y-axis we get

(-x,y)

Now, since we get (-x,y) when reflected along x-axis we get

(-x,-y)

So, our coordinate (-x,-y) will become (x,y) after rotated
`180^(\circ)`.

Therefore, Option A is correct.

Answer 2

"Reflect over the y-axis, reflect over the x-axis, rotate 180°" is the set of reflections and rotations among the choices given in the question that would carry rectangle ABCD onto itself. The correct option among all the options that are given in the question is the first option or option "A". I hope it helps you.