Question

Which transformation gives the same result as a reflection over the y-axis followed by a reflection over the x-axis?

a.A rotation of 180° around the origin
b.A rotation of 270° around the origin
c.A translation to the left and then down
d.A rotation of 90° around the origin

Answer 1

The correct answer is A

Answer 2

a. A rotation of 180° around the origin.

Explanation:

A rotation of 180° around the origin would give us the same result as a reflection over the y-axis followed by a reflection over the x-axis. When we perform this rotation, we take each of its points through the transformation (x,y) ---> (-x, -y). This means that we would multiply the coordinates of each of the points on the shape by a negative. This is equivalent to reflecting a shape over the x-axis and the y-axis.