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

Answer 1

When you perform a reflection across the x-axis followed by a reflection across the y-axis, you can analyze the effect on a point \((x, y)\):

1. Reflection across the x-axis: This transformation changes the y-coordinate, resulting in the point \((x, -y)\).
2. Reflection across the y-axis: This transformation changes the x-coordinate of the point obtained after the first reflection, resulting in the point \((-x, -y)\).

Therefore, the combined effect of these two reflections is to transform the point \((x, y)\) into \((-x, -y)\).

This transformation \((-x, -y)\) is equivalent to a rotation of 180 degrees about the origin. Thus, the composition of reflections across the x-axis and y-axis results in the same image as a rotation of 180 degrees about the origin.