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:

Analyze the first transformation mapping ABCDE to A'B'C'D'E'

$$ \text{Figure } ABCDE \xrightarrow{r_m} A'B'C'D'E' $$

$$ \text{This is a reflection across line } m. $$

Analyze the second transformation mapping A'B'C'D'E' to A''B''C''D''E''

$$ A'B'C'D'E' \xrightarrow{R_{C', 180^\circ}} A''B''C''D''E'' $$

$$ \text{This is a rotation of } 180^\circ \text{ about point } C'. $$

Write the composition of transformations

$$ (R_{C', 180^\circ} \circ r_m)(ABCDE) = A''B''C''D''E'' $$

Answer:

• (A) \(R_{C', 90^\circ} \circ r_m\)
• (B) \(r_m \circ R_{C', 90^\circ}\)
• (C) \(R_{C', 180^\circ} \circ r_m\) (Correct answer)
• (D) \(r_m \circ R_{C', 180^\circ}\)