Question

1. graph the image of △fga after a reflection over the line y = x.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the line $y = x$ is $(x,y)\to(y,x)$.

Step2: Identify vertices of $\triangle FGH$

Let's assume the coordinates of the vertices of $\triangle FGH$ are $F(x_1,y_1)$, $G(x_2,y_2)$ and $H(x_3,y_3)$. From the graph, if $F(-6,3)$, $G(1,3)$ and $H(-2,9)$.

Step3: Apply reflection rule to each vertex

For point $F(-6,3)$, after reflection over $y = x$, the new - point $F'(3,-6)$.
For point $G(1,3)$, after reflection over $y = x$, the new - point $G'(3,1)$.
For point $H(-2,9)$, after reflection over $y = x$, the new - point $H'(9,-2)$.

Step4: Plot the new triangle

Plot the points $F'(3,-6)$, $G'(3,1)$ and $H'(9,-2)$ and connect them to form the reflected triangle.

Answer:

Plot the points $F'(3,-6)$, $G'(3,1)$ and $H'(9,-2)$ and connect them to get the image of $\triangle FGH$ after reflection over the line $y = x$.