Question

square pqrs is transformed as shown on the graph. which rule describes the transformation? r0,90° r0,180° r0,270° r0,360°

Explanation:

Step1: Recall rotation rules

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

Step2: Analyze the transformation

Let's assume a point \(P(x,y)\) in square \(PQRS\). After transformation to \(P'(x',y')\) in the new square. If we observe the position of the square \(PQRS\) and its image, we can see that each point \((x,y)\) of square \(PQRS\) is mapped to \((-x,-y)\) in the image square. This is the rule for a \(180^{\circ}\) rotation about the origin.

Answer:

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