Question

which transformation would take figure a to figure b? answer a counterclockwise rotation of 180° about the origin a reflection over the line y = -x a counterclockwise rotation of 270° about the origin a reflection over the line y = x

Explanation:

Step1: Recall rotation and reflection rules

For a point $(x,y)$:

• A counter - clockwise rotation of $180^{\circ}$ about the origin gives $(-x,-y)$.
• A reflection over the line $y = -x$ swaps and negates the coordinates, giving $(-y,-x)$.
• A counter - clockwise rotation of $270^{\circ}$ about the origin is equivalent to a clockwise rotation of $90^{\circ}$, and for a point $(x,y)$ gives $(y,-x)$.
• A reflection over the line $y = x$ swaps the coordinates, giving $(y,x)$.

Step2: Analyze the orientation of Figure A and Figure B

Let's assume a general point on Figure A with coordinates $(x,y)$. By observing the orientation of Figure A and Figure B, we can see that if we take a point $(x,y)$ on Figure A and want to get the corresponding point on Figure B, the transformation is a counter - clockwise rotation of $270^{\circ}$ about the origin. For example, if we consider a right - most point of Figure A with positive $x$ and negative $y$ coordinates, after a counter - clockwise rotation of $270^{\circ}$ about the origin, its new coordinates $(y,-x)$ match the position of the corresponding point on Figure B.

Answer:

A counter - clockwise rotation of $270^{\circ}$ about the origin