Question

triangle xyz has vertices x(1, 3), y(0, 0), and z(-1, 2). the image of triangle xyz after a rotation has vertices x(-3, 1), y(0, 0), and z(-2, -1). which rule describes the transformation?
○ r₀, 90°
○ r₀, 150°
○ r₀, 270°
○ r₀, 180°

Explanation:

Step1: Recall rotation rules

The rule for a \( 90^{\circ}\) rotation about the origin \((x,y)\to(-y,x)\).

Step2: Apply the rule to a vertex

For vertex \(X(1,3)\), using the rule \((x,y)\to(-y,x)\), we substitute \(x = 1\) and \(y=3\). Then \(-y=-3\) and \(x = 1\), so the image is \(X'(-3,1)\).

Step3: Check another vertex

For vertex \(Z(-1,2)\), using the rule \((x,y)\to(-y,x)\), substitute \(x=-1\) and \(y = 2\). Then \(-y=-2\) and \(x=-1\), so the image is \(Z'(-2,-1)\).

Since the transformation rule \((x,y)\to(-y,x)\) (which is \(R_{0,90^{\circ}}\)) works for the given vertices, the answer is \(R_{0,90^{\circ}}\).

Answer:

\( R_{0, 90^{\circ}} \)