Question

triangle xyz with vertices x(0,0), y(0,-2), and z(-2,-2) is rotated to create the image triangle x(0,0), y(2,0), and z(2,-2). which rules could describe the rotation? select two options
□ r_0, 90°
□ r_0, 180°
□ r_0, 270°
□ (x,y)→(-y,x)
□ (x,y)→(y,-x)

Explanation:

Step1: Recall rotation rules

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).

Step2: Check each vertex

For \(Y(0, - 2)\): Using the rule \((x,y)\to(-y,x)\), we substitute \(x = 0\) and \(y=-2\). Then \((0,-2)\to(2,0)\) (since \(-y=-(-2) = 2\) and \(x = 0\)).
For \(Z(-2,-2)\): Substitute \(x=-2\) and \(y = - 2\) into \((x,y)\to(-y,x)\), we get \((-2,-2)\to(2,-2)\) (since \(-y=-(-2)=2\) and \(x=-2\)).
The rotation \(R_{0,270^{\circ}}\) is equivalent to the transformation \((x,y)\to(-y,x)\)

Answer:

C. \(R_{0,270^{\circ}}\), D. \((x,y)\to(-y,x)\)