Question

which rule describes the composition of transformations that maps \\(\delta abc\\) to \\(\delta abc\\)?

\\(r_{o,\\, 90^{\circ}} \circ r_{x-\text{axis}}(x, y)\\)
\\(r_{x-\text{axis}} \circ r_{o,\\, 90^{\circ}}(x, y)\\)
\\(r_{o,\\, 180^{\circ}} \circ r_{x-\text{axis}}(x, y)\\)
\\(r_{x-\text{axis}} \circ r_{o,\\, 180^{\circ}}(x, y)\\)

Explanation:

Identify coordinates of the original and final figures

Using the Coordinate Reflections knowledge point

$$
LATEXBLOCK0
$$

Test the first transformation sequence

Using the Coordinate Reflections and Rotations about Origin knowledge points

$$
LATEXBLOCK1
$$

Test the second transformation sequence

Using the Rotations about Origin and Coordinate Reflections knowledge points

$$
LATEXBLOCK2
$$

Verify the correct mapping rule

Using the Coordinate Reflections and Rotations about Origin knowledge points

$$
LATEXBLOCK3
$$

Answer:

• (A) \(R_{O, 90^\circ} \circ r_{x-\text{axis}}(x, y)\)
• (B) \(r_{x-\text{axis}} \circ R_{O, 90^\circ}(x, y)\) (Correct answer)
• (C) \(R_{O, 180^\circ} \circ r_{x-\text{axis}}(x, y)\)
• (D) \(r_{x-\text{axis}} \circ R_{O, 180^\circ}(x, y)\)