Question

rectangle \\(efgh\\) is graphed on a coordinate grid. \\(efgh\\) is transformed according to the rule \\(r_{0, 180^{\circ}}\\), resulting in rectangle \\(efgh\\).

which transformation or composition of transformations will produce the same result?

\\(r_{\text{x-axis}} \circ r_{\text{y-axis}}\\)
\\(r_{y = x}\\)
\\(r_{0, 270^{\circ}} \circ r_{0, 90^{\circ}}\\)
\\(r_{0, 90^{\circ}} \circ r_{0, 270^{\circ}}\\)

Explanation:

Analyze the target transformation

$$ R_{O, 180^\circ}(x, y) = (-x, -y) $$

Evaluate the first option

$$
LATEXBLOCK0
$$

Evaluate the remaining options

$$
LATEXBLOCK1
$$

Answer:

• (A) \(r_{x\text{-axis}} \circ r_{y\text{-axis}}\) (Correct answer)
• (B) \(r_{y = x}\)
• (C) \(R_{O, 270^\circ} \circ R_{O, 90^\circ}\)
• (D) \(R_{O, 90^\circ} \circ R_{O, 270^\circ}\)