Question

1. rotation 180° about the origin
2. reflection across the x - axis

Explanation:

Step1: Recall rotation rule

A 180 - degree rotation about the origin changes the sign of both the x - and y - coordinates of each point.

Step2: Analyze each option for 180 - degree rotation

Check the orientation and position of the figure in each option after applying the 180 - degree rotation rule. Option B shows the correct orientation and position of the figure after a 180 - degree rotation about the origin.

Step3: Recall reflection rule

A reflection across the x - axis changes the sign of the y - coordinate of each point while the x - coordinate remains the same.

Step4: Analyze each option for reflection

Check the orientation and position of the figure in each option after applying the reflection - across - the - x - axis rule. Option C shows the correct orientation and position of the figure after a reflection across the x - axis.

Answer:

1. B
2. C