Question

triangle xyz is rotated to create the image triangle xyz. 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)→(-x,-y)

Explanation:

Step1: Recall rotation rules

• \(R_{0,90^{\circ}}\): \((x,y)\to(-y,x)\)
• \(R_{0,180^{\circ}}\): \((x,y)\to(-x,-y)\)
• \(R_{0,270^{\circ}}\): \((x,y)\to(y,-x)\)

Step2: Analyze the rotation

Let's assume a point, say \(Z(0,4)\). After rotation, \(Z'\) is \((0, - 4)\). Let \(X(-2,2)\), after rotation \(X'(2,-2)\). Let \(Y(2,2)\), after rotation \(Y'(-2,-2)\)

• For \(R_{0,180^{\circ}}\), if \((x,y)\) is a point, then \((x,y)\to(-x,-y)\). For \(Z(0,4)\), \((0,4)\to(0,-4)\); for \(X(-2,2)\), \((-2,2)\to(2,-2)\); for \(Y(2,2)\), \((2,2)\to(-2,-2)\)
• The rule \((x,y)\to(-x,-y)\) is equivalent to \(R_{0,180^{\circ}}\)

Answer:

\(R_{0,180^{\circ}}\), \((x,y)\to(-x,-y)\)