Question

figure d is the result of a transformation on figure c. which transformation would accomplish this? answer a reflection over the x -axis a rotation 90° clockwise about the origin a reflection over the y -axis a rotation 90° counterclockwise about the origin

Explanation:

Step1: Recall reflection rules

A reflection over the x - axis changes the sign of the y - coordinate of each point. A reflection over the y - axis changes the sign of the x - coordinate of each point. A 90 - degree clockwise rotation about the origin has the transformation rule \((x,y)\to(y, - x)\) and a 90 - degree counter - clockwise rotation about the origin has the transformation rule \((x,y)\to(-y,x)\).

Step2: Analyze the figure

If we look at the orientation of Figure C and Figure D, we can see that if we take a point \((x,y)\) on Figure C and apply a 90 - degree clockwise rotation about the origin \((x,y)\to(y,-x)\), we get the corresponding point on Figure D. For example, if a point on Figure C has coordinates \((3,5)\), after a 90 - degree clockwise rotation about the origin, it becomes \((5, - 3)\) which is consistent with the transformation from Figure C to Figure D.

Answer:

A rotation 90° clockwise about the origin