Question

triangle gfh has vertices $g(2, -3)$, $f(4, -1)$, and $h(1, 1)$. the triangle is rotated $270^{\circ}$ clockwise using the origin as the center of rotation. which graph shows the rotated image?

Explanation:

Step1: Recall 270° clockwise rotation rule

A point $(x,y)$ rotated 270° clockwise about the origin transforms to $(-y, x)$.

Step2: Calculate new coordinates for G

For $G(2,-3)$: $x=2, y=-3$. New point $G' = -(-3), 2 = (3, 2)$.

Step3: Calculate new coordinates for F

For $F(4,-1)$: $x=4, y=-1$. New point $F' = -(-1), 4 = (1, 4)$.

Step4: Calculate new coordinates for H

For $H(1,1)$: $x=1, y=1$. New point $H' = -(1), 1 = (-1, 1)$.

Answer:

The correct graph is the lower one, with vertices $G'(3,2)$, $F'(1,4)$, and $H'(-1,1)$.