Question

What set of reflections would carry parallelogram ABCD onto itself?

a) X-axis, y=x, X-axis, y=x
b) y=x, X-axis, y=x, y-axis
c) y-axis, X-axis, y-axis
d) None of the above

Answer 1

The set of reflections that would carry parallelogram ABCD onto itself is y=x, X-axis, y=x, y-axis (option b).

Step-by-step explanation:

The set of reflections that would carry parallelogram ABCD onto itself is y=x, X-axis, y=x, y-axis (option b).

When you reflect a shape in the x-axis, all the points of the shape are reflected across the x-axis. Similarly, when you reflect a shape in the y-axis, all the points of the shape are reflected across the y-axis. And when you reflect a shape in the line y=x, all the points of the shape are reflected across the line y=x.

In option b, parallelogram ABCD is reflected first in the line y=x, then in the x-axis, then in the line y=x again, and finally in the y-axis. This set of reflections would carry parallelogram ABCD onto itself.