Question

which transformation would take figure a to figure b? answer a reflection over the line y = -x a counterclockwise rotation of 180° about the origin a counterclockwise rotation of 90° about the origin a reflection over the line y = x

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ rotated 180° counter - clockwise about the origin, the new point is $(-x,-y)$. For reflection over $y = - x$, the transformation is $(x,y)\to(-y,-x)$; for 90° counter - clockwise rotation about the origin, $(x,y)\to(-y,x)$; for reflection over $y = x$, $(x,y)\to(y,x)$.

Step2: Analyze Figure A and B

By observing the position of Figure A and Figure B, we can see that the orientation of Figure A is reversed to get Figure B. If we take a general point on Figure A and apply a 180° counter - clockwise rotation about the origin, it will map to the corresponding point on Figure B. For example, if a point on Figure A has coordinates $(x,y)$, after 180° counter - clockwise rotation about the origin, it becomes $(-x,-y)$ which is consistent with the position of the corresponding point on Figure B.

Answer:

B. A counterclockwise rotation of 180° about the origin