Question

which rule describes the composition of transformations that maps figure abcde to figure a\b\c\d\e\?
$r_{c,90^{circ}}circ r_{m}$
$r_{m}circ r_{c,90^{circ}}$
$r_{c,180^{circ}}circ r_{m}$
$r_{m}circ r_{c,180^{circ}}$

Explanation:

Step1: Analyze transformation order

First, we need to determine if reflection or rotation occurs first. Looking at the figures, it seems that a reflection across line \(m\) occurs first, followed by a rotation. The notation \(r_m\) represents reflection across line \(m\) and \(R_{C',\theta}\) represents rotation about point \(C'\) by an angle \(\theta\).

Step2: Determine rotation angle

By observing the orientation of the final figure \(A''B''C''D''E''\) relative to the figure after reflection, we can see that the rotation angle is \(180^{\circ}\) about point \(C'\).

Answer:

\(R_{C',180^{\circ}}\circ r_m\)