Question

which transformation would result in the same image as a composition transformation of reflections across the x - axis and then the y - axis? (1 point)

a 90 - degree rotation

a 180 - degree rotation

a reflection

a dilation

Explanation:

Step1: Recall reflection properties

Reflection across x - axis changes $(x,y)$ to $(x, - y)$. Reflection across y - axis changes $(x,-y)$ to $(-x,-y)$.

Step2: Recall rotation properties

A 180 - degree rotation about the origin changes a point $(x,y)$ to $(-x,-y)$. So, a composition of reflections across the x - axis and then the y - axis is equivalent to a 180 - degree rotation about the origin.

Answer:

B. a 180 - degree rotation