Question

identifying a rotation tell whether the blue figure is a rotation of the red figure about the origin. if so, give the angle and direction of rotation.
9.
10.
11.
12.

Explanation:

Step1: Recall rotation rules

For a 180 - degree rotation about the origin, \((x,y)\to(-x,-y)\).

Step2: Analyze figure 9

Check corresponding points. If blue figure is \((x,y)\) and red is \((-x,-y)\), it's a 180 - degree rotation.

Step3: Analyze figure 10

Corresponding points do not follow \((x,y)\to(-x,-y)\) rule.

Step4: Analyze figure 11

Check points. They follow the 180 - degree rotation rule \((x,y)\to(-x,-y)\).

Step5: Analyze figure 12

Points of blue and red figures follow \((x,y)\to(-x,-y)\) for 180 - degree rotation.

Answer:

1. Yes, 180 - degree rotation about the origin.
2. No.
3. Yes, 180 - degree rotation about the origin.
4. Yes, 180 - degree rotation about the origin.