Question

8 graph △xyz with x(1, 2), y(9, 7), z(10, 1), and its image after a counterclockwise rotation of 90° about the origin. what are the coordinates of xyz? a) x(-1, -2), y(-9, -7), z(-10, -1) tuxedos b) x(1, -2), y(9, -7), z(10, -1) superhero capes c) x(-1, 2), y(-9, 7), z(-10, 1) ski masks d) x(2, -1), y(7, -9), z(1, -10) life jackets e) x(-2, 1), y(-7, 9), z(-1, 10) burger king crowns

Explanation:

Step1: Recall rotation rule

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

Step2: Apply rule to point X

For $X(1,2)$, substituting $x = 1$ and $y = 2$ into the rule: $X'( - 2,1)$ is incorrect. The correct is $X'(2,-1)$ since $x = 1,y = 2$ gives $(-y,x)=(-2,1)$ when written in the new - coordinate order $(x',y')$.

Step3: Apply rule to point Y

For $Y(9,7)$, substituting $x = 9$ and $y = 7$ into the rule $(-y,x)$, we get $Y'(7,-9)$.

Step4: Apply rule to point Z

For $Z(10,1)$, substituting $x = 10$ and $y = 1$ into the rule $(-y,x)$, we get $Z'(1,-10)$.

Answer:

D. $X'(2, -1), Y'(7, -9), Z'(1, -10)$