Which transformation would result in the same image as a composition transformation of reflections across the x-axis and then the y-axis?

Question

a. a 180-degree rotation
b. a reflection
c. a 90-degree rotation
d. a dilation

Answer 1

The composition of transformations of reflections across the x-axis and then the y-axis results in a 180-degree rotation.

When you reflect a point over the x-axis, you negate the y-coordinate, and when you reflect that resulting point over the y-axis, you negate the x-coordinate. The result is that both coordinates are negated, which is equivalent to rotating the point 180 degrees around the origin.

So, the correct answer is:

a. a 180-degree rotation.