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 rotation or reflection occurs first. Looking at the figure, we can see that a rotation about a center \(C\) seems to happen first and then a reflection across line \(m\). The notation \(R_{C,\theta}\) represents a rotation about center \(C\) by an angle \(\theta\) and \(r_m\) represents a reflection across line \(m\).

Step2: Determine rotation angle

By observing the orientation change of the figure, we can tell that the rotation angle is \(90^{\circ}\) counter - clockwise (assuming the standard convention). So the rotation is \(R_{C,90^{\circ}}\).

Step3: Determine composition notation

The composition of transformations where we first rotate and then reflect is written as \(r_m\circ R_{C,90^{\circ}}\). The symbol \(\circ\) means to perform the transformation on the right first and then the one on the left.

Answer:

\(r_m\circ R_{C,90^{\circ}}\) (corresponding to the second option in the multiple - choice list)