Question

a sequence of rigid motions was performed on △abc that maps to △rst. which transformation maps △abc onto △rst? a. rotate△abc90° clockwise about the origin b. rotate△abc90° clockwise about point c c. translate△abc2 units to the right and 2 units down d. translate△abc7 units to the right and 3 units down

Explanation:

Step1: Analyze translation

Translation only moves the figure without rotation. If we consider option C (translate 2 units right and 2 units down) or D (translate 7 units right and 3 units down), the orientation of the triangle would remain the same. But from the figure (assuming standard grid - based orientation analysis), the orientation of $\triangle ABC$ and $\triangle RST$ is different, so translation (options C and D) is not the correct transformation.

Step2: Analyze rotation about a point

Rotation about a point changes the orientation of the figure. If we rotate about the origin, every point of the triangle $\triangle ABC$ is rotated with respect to the origin. If we rotate about point $C$, point $C$ remains fixed.
Let's assume we use the rule for rotation about the origin. The rule for a $90^{\circ}$ clock - wise rotation about the origin is $(x,y)\to(y, - x)$. If we consider the coordinates of the vertices of $\triangle ABC$ and apply the rotation rule, we can see that it will map $\triangle ABC$ to $\triangle RST$. Rotation about point $C$ (option B) will not map $\triangle ABC$ to $\triangle RST$ as the position of other vertices (relative to a non - origin center of rotation) will not match the figure's mapping.

Answer:

A. rotate $\triangle ABC90^{\circ}$ clockwise about the origin