Question

the vertices for triangle abc are (2, 1), (3, 5) and (5, 3). the triangle will be rotated 90° counterclockwise about the origin. where will triangle abc be after being rotated?

Explanation:

Step1: Recall rotation rule

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

Step2: Rotate point A

For point $A(2,1)$, using the rule $(x,y)\to(-y,x)$, we get $A'(-1,2)$.

Step3: Rotate point B

For point $B(3,5)$, using the rule $(x,y)\to(-y,x)$, we get $B'(-5,3)$.

Step4: Rotate point C

For point $C(5,3)$, using the rule $(x,y)\to(-y,x)$, we get $C'(-3,5)$.

Answer:

The vertices of $\triangle A'B'C'$ are $A'(-1,2)$, $B'(-5,3)$ and $C'(-3,5)$.