Question

What set of reflections would carry parallelogram ABCD onto itself?

x-axis, y=x, y-axis, x-axis

x-axis, y-axis, x-axis

y-axis, x-axis, y-axis, x-axis

y=x, x-axis, x-axis

Answer 1

The correct answer is:

y-axis, x-axis, y-axis, x-axis .

Step-by-step explanation:

A reflection across the y-axis negates the x-coordinate; algebraically,

(x, y)→(-x, y).

A reflection across the x-axis negates the y-coordinate; algebraically, this takes our new point

(-x, y)→(-x, -y).

Reflecting again across the y-axis will take our new point

(-x, -y)→(x, -y).

Reflecting again across the x-axis will take our new point

(x, -y)→(x, y).

This is where we started; thus the polygon is mapped onto itself.

Answer 2

"y-axis, x-axis, y-axis, x-axis" is the set of reflections among the following choices given in the question that would carry parallelogram ABCD onto itself. The correct option among all the options that are given in the question is the third option or the penultimate option. I hope that this is the answer that has helped you.