Question

1. rotate the triangle 90° counterclockwise about the origin.

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 original points

Assume the vertices of the triangle are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$. Let's say from the graph, $A(1,6)$, $B(2,1)$, $C(8,2)$.

Step3: Apply rotation rule to point A

For $A(1,6)$, using the rule $(x,y)\to(-y,x)$, we get $A'(-6,1)$.

Step4: Apply rotation rule to point B

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

Step5: Apply rotation rule to point C

For $C(8,2)$, using the rule $(x,y)\to(-y,x)$, we get $C'(-2,8)$.

Answer:

The new vertices of the rotated triangle are $A'(-6,1)$, $B'(-1,2)$, $C'(-2,8)$.