Question

for each set of figures, figure a is rotated around the origin to form figure b. drag each set of figures into a box to identify the rotation that it represents. answer choices may be used more than once. 90° clockwise 90° counterclockwise 180° clockwise 180° counterclockwise 270° clockwise 270° counterclockwise

Explanation:

Step1: Recall rotation rules

For a 90 - degree clockwise rotation of a point (x,y) around the origin, the new coordinates are (y, - x). For a 90 - degree counter - clockwise rotation, new coordinates are (-y,x). For a 180 - degree rotation (clockwise or counter - clockwise), new coordinates are (-x,-y). For a 270 - degree clockwise rotation, new coordinates are (-y,x) and for a 270 - degree counter - clockwise rotation, new coordinates are (y, - x).

Step2: Analyze first pair of figures

In the first pair of figures (left - most in the bottom row), figure A is rotated 90 degrees counter - clockwise to get figure B. We can check by looking at the orientation of the shape and comparing key points.

Step3: Analyze second pair of figures

In the second pair of figures, figure A is rotated 180 degrees (either clockwise or counter - clockwise since they are equivalent for a 180 - degree rotation) to get figure B.

Step4: Analyze third pair of figures

In the third pair of figures, figure A is rotated 270 degrees counter - clockwise (or 90 degrees clockwise) to get figure B.

Answer:

First pair: 90° counterclockwise
Second pair: 180° clockwise (or 180° counterclockwise)
Third pair: 270° counterclockwise