Question

square pqrs is transformed as shown on the graph. which rule describes the transformation? ( r_{0,90^{circ}} ) ( r_{0,180^{circ}} ) ( r_{0,270^{circ}} ) ( r_{0,360^{circ}} )

Explanation:

Step1: Recall rotation rules

• Rotation of \(90^{\circ}\) about the origin: \((x,y)\to(-y,x)\)
• Rotation of \(180^{\circ}\) about the origin: \((x,y)\to(-x,-y)\)
• Rotation of \(270^{\circ}\) about the origin: \((x,y)\to(y, -x)\)
• Rotation of \(360^{\circ}\) about the origin: \((x,y)\to(x,y)\)

Let's assume a point \(Q(2,2)\) in the original square. After transformation, \(Q'\) is \((- 2,-2)\)

Step2: Apply rotation rules

If we apply the \(180^{\circ}\) rotation rule \((x,y)\to(-x,-y)\) to the point \(Q(2,2)\), we get \((-2,-2)\) which matches the transformed point \(Q'\)

Answer:

\(R_{0,180^{\circ}}\)