Question

a (-4,-2) c (-1,-2) b (1,-3) a (2,-4) describe the transformation in the diagram. (1 point) 90° clockwise rotation about the origin 270° counter - clockwise rotation about the origin 180° counter - clockwise rotation about the origin 90° counter - clockwise rotation about the origin

Explanation:

Step1: Recall rotation rules

For a 90 - degree clockwise rotation about the origin, the rule is $(x,y)\to(y, - x)$. For a 270 - degree counter - clockwise rotation about the origin (same as 90 - degree clockwise), the rule is $(x,y)\to(y, - x)$. For a 180 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-x,-y)$. For a 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$.

Step2: Check point A transformation

Point $A(-4,-2)$ and its image $A'(2, - 4)$. Using the 90 - degree clockwise rotation rule $(x,y)\to(y,-x)$, when $x=-4$ and $y = - 2$, we get $(y,-x)=(-2,4)$ which is incorrect. Using the 270 - degree counter - clockwise rotation rule (same as 90 - degree clockwise) is incorrect as above. Using the 180 - degree counter - clockwise rotation rule, $(-4,-2)\to(4,2)$ which is incorrect. Using the 90 - degree counter - clockwise rotation rule, for $A(-4,-2)$, $x=-4$ and $y=-2$, then $(-y,x)=(2,-4)$ which matches $A'$.

Step3: Check point B' transformation (we can also check other points). Let's assume there was a pre - image of $B'$. But checking $A$ is sufficient. The transformation rule of 90 - degree counter - clockwise rotation holds for the given transformation.

Answer:

90° counterclockwise rotation about the origin