Question

figure c figure b answer a rotation 90° clockwise about the origin a translation 4 units to the left and 4 units up a translation 4 units to the right and 4 units down a rotation 90° counterclockwise about the origin

Explanation:

Step1: Recall rotation and translation rules

For a 90 - degree clockwise rotation about the origin $(x,y)\to(y, - x)$. For a 90 - degree counter - clockwise rotation about the origin $(x,y)\to(-y,x)$. For a translation $a$ units left and $b$ units up, $(x,y)\to(x - a,y + b)$ and for a translation $a$ units right and $b$ units down, $(x,y)\to(x + a,y - b)$.

Step2: Analyze the transformation from Figure B to Figure C

Let's take a point on Figure B, say the top - right vertex of Figure B which is at $(2,1)$. If we consider a 90 - degree counter - clockwise rotation about the origin, using the rule $(x,y)\to(-y,x)$, for the point $(2,1)$ we get $(-1,2)$. If we consider a 90 - degree clockwise rotation about the origin, using the rule $(x,y)\to(y, - x)$, for the point $(2,1)$ we get $(1,-2)$. If we consider a translation 4 units right and 4 units down, for the point $(2,1)$ we get $(2 + 4,1-4)=(6,-3)$. If we consider a translation 4 units left and 4 units up, for the point $(2,1)$ we get $(2-4,1 + 4)=(-2,5)$.
By observing the orientation and position of Figure C relative to Figure B, we can see that the transformation from Figure B to Figure C is a translation 4 units to the left and 4 units up.

Answer:

A translation 4 units to the left and 4 units up