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^{circ}} □ r_{0,180^{circ}} □ r_{0,270^{circ}} □ (x, y) → (-y, x) □ (x, y) → (y, -x)

Explanation:

Step1: Recall rotation rules

• Rotation of \(90^{\circ}\) clockwise: \((x,y)\to(y, - x)\)
• Rotation of \(180^{\circ}\): \((x,y)\to(-x,-y)\)
• Rotation of \(270^{\circ}\) clockwise: \((x,y)\to(-y,x)\)

Step2: Apply rules to vertices

• For \(Y(0,-2)\):
• If we use \(R_{0,270^{\circ}}\) (rotation of \(270^{\circ}\) clockwise about the origin), using the rule \((x,y)\to(-y,x)\), for \(Y(0, - 2)\), we get \((-(-2),0)=(2,0)\) which is \(Y'\)
• If we use the rule \((x,y)\to(-y,x)\) (equivalent to \(270^{\circ}\) clockwise rotation about the origin) for \(Y(0,-2)\) gives \((2,0)\)

Answer:

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