Question

triangle qrs is transformed as shown on the graph. which rule describes the transformation? o $r_{0,90^{circ}}$ o $r_{0,180^{circ}}$ o $r_{0,270^{circ}}$ o $r_{0,360^{circ}}$

Explanation:

Step1: Recall rotation rules

The rule for a rotation of $R_{0,\theta}$ about the origin $(0,0)$:

• For $R_{0,90^{\circ}}$: $(x,y)\to(-y,x)$
• For $R_{0,180^{\circ}}$: $(x,y)\to(-x,-y)$
• For $R_{0,270^{\circ}}$: $(x,y)\to(y, - x)$
• For $R_{0,360^{\circ}}$: $(x,y)\to(x,y)$

Step2: Analyze the transformation

By observing the graph, we can take a point, say $Q(3,1)$. Its image $Q'(- 3,-1)$. If we apply the rule $(x,y)\to(-x,-y)$ (which is the rule for a $180^{\circ}$ rotation about the origin) to the point $(3,1)$, we get $(-3,-1)$.

Answer:

$R_{0,180^{\circ}}$