Question

describe the transformation in the diagram (1 point) o 90° clockwise rotation about the origin o 270° counter - clockwise rotation about the origin o 180° counter - clockwise rotation about the origin o 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, the rule is also $(x,y)\to(y, - x)$. 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 $A(-4,-2)$ is transformed to $A'(2, - 4)$. Using the rule $(x,y)\to(y, - x)$ for 90 - degree clockwise or 270 - degree counter - clockwise rotation: when $x=-4$ and $y = - 2$, $( - 4,-2)\to(-2,4)$ which is wrong. Using the rule $(x,y)\to(-x,-y)$ for 180 - degree counter - clockwise rotation: $(-4,-2)\to(4,2)$ which is wrong. Using the rule $(x,y)\to(-y,x)$ for 90 - degree counter - clockwise rotation: when $x=-4$ and $y=-2$, $(-4,-2)\to(2,-4)$ which is correct.

Step3: Check other points

For point $B(-3,-1)$, using the 90 - degree counter - clockwise rotation rule $(x,y)\to(-y,x)$, when $x = - 3$ and $y=-1$, $(-3,-1)\to(1,-3)$ which is correct. For point $C(-1,-2)$, using the 90 - degree counter - clockwise rotation rule $(x,y)\to(-y,x)$, when $x=-1$ and $y = - 2$, $(-1,-2)\to(2,-1)$ which is correct.

Answer:

90° counterclockwise rotation about the origin