Question

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

Explanation:

Step1: Recall rotation and reflection rules

Rotation and reflection are geometric transformations. For rotation about the origin, a 90 - degree counter - clockwise rotation of a point $(x,y)$ gives $(-y,x)$ and a 180 - degree counter - clockwise rotation gives $(-x,-y)$. For reflection over $y = x$, the point $(x,y)$ becomes $(y,x)$ and over $y=-x$ it becomes $(-y,-x)$.

Step2: Analyze the orientation of Figure A and Figure B

By observing the orientation of the two figures, if we take a general point $(x,y)$ on Figure A and consider a 180 - degree counter - clockwise rotation about the origin, its new coordinates $(-x,-y)$ will match the position of the corresponding point on Figure B.

Answer:

A counterclockwise rotation of 180 about the origin