Question

triangle rst has vertices r(2, 0), s(4, 0), and t(1, -3). the image of triangle rst after a rotation has vertices r(0, -2), s(0, -4), and t(-3, -1). which rule describes the transformation?

\\(r_{0, 90^\circ}\\)
\\(r_{0, 180^\circ}\\)
\\(r_{0, 270^\circ}\\)
\\(r_{0, 360^\circ}\\)

Explanation:

Identify the coordinate mapping

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK0
$$

Determine the general transformation rule

Using the Geometric Transformations knowledge point

$$ (x, y) \to (y, -x) $$

Match the rule to a standard rotation

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK1
$$

Thus, the transformation is a counterclockwise rotation of \(270^\circ\) about the origin.

Answer:

• (A) \(R_{O, 90^\circ}\)
• (B) \(R_{O, 180^\circ}\)
• (C) \(R_{O, 270^\circ}\) (Correct answer)
• (D) \(R_{O, 360^\circ}\)