Question

cedric applied the rule $r_m \circ r_{p, 90\degree}(x, y)$ to figure wxyz. what mistakes did he make? select two options. he applied the reflection to the pre - image first. he applied the rotation to the pre - image first. he changed the size of the figure instead of just applying a rotation. he used point p as the center of rotation. he used an incorrect angle of rotation around point p.

Explanation:

In a composition of transformations \(r_{m}\circ R_{P,360^{\circ}}\), the notation \(r_{m}\circ R_{P,360^{\circ}}\) means first perform the rotation \(R_{P,360^{\circ}}\) (rotation about point \(P\) by \(360^{\circ}\)) and then the reflection \(r_{m}\) (reflection over line \(m\)). But Cedric did the reflection first. Also, a \(360^{\circ}\) rotation about a point \(P\) should map a figure onto itself. If he used point \(P\) as the center of rotation, a \(360^{\circ}\) rotation about \(P\) would not change the position of the figure (since rotating a figure \(360^{\circ}\) about a point brings it back to its original position). But from the figure, it seems he did not use the correct center (if he had used \(P\) as the center of rotation for \(360^{\circ}\), the figure before reflection would be in the same position as the pre - image).

Answer:

He applied the reflection to the pre - image first. ; He used point \(P\) as the center of rotation.