Question

transformations rotations describe the transformation in the diagram. (1 point) 90° clockwise rotation about the origin 90° counterclockwise rotation about the origin 270° counterclockwise rotation about the origin 180° counterclockwise 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 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$. For a 270 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(y, - x)$ (same as 90 - degree clockwise), and for a 180 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-x,-y)$.

Step2: Check point A transformation

Point $A(-4,-2)$ is transformed to $A'(2, - 4)$. Using the rule $(x,y)\to(y, - x)$ (90 - degree clockwise or 270 - degree counter - clockwise), when $x=-4$ and $y = - 2$, we get $y=-2$ and $-x = 4$, which is correct for 90 - degree clockwise rotation.

Step3: Check point B transformation

Point $B(-3,-1)$ is transformed to $B'(1,-3)$. Using the rule $(x,y)\to(y, - x)$, when $x=-3$ and $y=-1$, we have $y=-1$ and $-x = 3$, which is consistent with 90 - degree clockwise rotation.

Step4: Check point C transformation

Point $C(-1,-2)$ is transformed to $C'(2,-1)$. Using the rule $(x,y)\to(y, - x)$, when $x=-1$ and $y=-2$, we get $y=-2$ and $-x = 1$, which is also consistent with 90 - degree clockwise rotation.

Answer:

90° clockwise rotation about the origin