Question

figure r figure s answer a reflection over the x -axis a translation 8 units to the right and 6 units down a rotation 180° clockwise about the origin a rotation 90° counterclockwise about the origin

Explanation:

Step1: Analyze reflection over x - axis

For a point $(x,y)$ reflected over the $x$-axis, the new point is $(x, -y)$. The orientation of the figure would change in a way that is not the case here.

Step2: Analyze translation

For a translation 8 units to the right and 6 units down, if a point in Figure R has coordinates $(x,y)$, the new coordinates in Figure S would be $(x + 8,y-6)$. Consider a vertex of Figure R, say $(-5,0)$. After translation 8 units right and 6 units down, it would be $(-5 + 8,0 - 6)=(3,-6)$. Check other vertices, and this transformation works for all of them.

Step3: Analyze rotation 180° clockwise

For a 180° clockwise rotation about the origin, if a point $(x,y)$ in Figure R, the new point is $(-x,-y)$. This does not match the transformation from Figure R to Figure S.

Step4: Analyze rotation 90° counter - clockwise

For a 90° counter - clockwise rotation about the origin, if a point $(x,y)$ in Figure R, the new point is $(-y,x)$. This does not match the transformation from Figure R to Figure S.

Answer:

A translation 8 units to the right and 6 units down