Question

graph the image of △fgh after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify vertices of $\triangle FGH$

Let's assume $F(5,0)$, $G(5,6)$, $H(3,1)$.

Step3: Apply rotation rule to $F$

For $F(5,0)$, using the rule $(x,y)\to(-y,x)$, we get $F'(0,5)$.

Step4: Apply rotation rule to $G$

For $G(5,6)$, $(x,y)\to(-y,x)$ gives $G'(-6,5)$.

Step5: Apply rotation rule to $H$

For $H(3,1)$, $(x,y)\to(-y,x)$ gives $H'(-1,3)$.

Step6: Graph new triangle

Plot the points $F'(0,5)$, $G'(-6,5)$ and $H'(-1,3)$ and connect them to form the new triangle.

Answer:

Graph the points $F'(0,5)$, $G'(-6,5)$ and $H'(-1,3)$ and connect them to get the image of $\triangle FGH$ after a 90 - degree counter - clockwise rotation around the origin.