8) which transformation will be equivalent to rotating a figure 90° counterclockwise?

For every point in the plane (x, y), a 90° rotation can be described by the transformation P(x, y) → P'(-y, x). We can achieve this same transformation by performing two reflections.

A reflection across the line y = x "swaps" the coordinates of every point so that every point P(x, y) transforms into a new point P'(y, x). If we follow this with a reflection across the y-axis, we can flip the sign of our x-coordinate, resulting in a new point P''(-y, x). To review:

comparing this to the effect of a 90° rotation:

We can see that the results are identical, so reflecting a figure across the line y = x and then across the y-axis is equivalent to rotating it 90° counterclockwise.

180 square centimeters

step-by-step explanation: