Question

1. rotation 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 coordinates of points in the triangle are $F(x_1,y_1)$, $G(x_2,y_2)$, $H(x_3,y_3)$. For example, if $F$ is at $( - 3,2)$, $G$ is at $( - 3,-2)$, and assume another point $H$ (not clearly labeled in the question but for general triangle rotation).

Step3: Apply rotation rule

For point $F(-3,2)$, after rotation, $F'$ is at $(-2,-3)$. For point $G(-3,-2)$, after rotation, $G'$ is at $(2,-3)$.

Answer:

The new coordinates of the vertices of the triangle after a 90 - degree counter - clockwise rotation about the origin can be found using the rule $(x,y)\to(-y,x)$ for each vertex.