Question

graph triangle xyz with x(-7, -9), y(-10, -3), z(-1, -9), and its image after a 90° counterclockwise rotation about the origin. what are the coordinates of z?

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Identify coordinates of Z

The coordinates of point $Z$ are $(-1,-9)$.

Step3: Apply rotation rule

For $Z(-1,-9)$, substituting $x=-1$ and $y = - 9$ into the rule $(-y,x)$, we get $-y=-(-9)=9$ and $x=-1$. So the new coordinates of $Z'$ are $(9,-1)$.

Answer:

$(9,-1)$