Question

graph the image of the polygon after a reflection in the line y = x.

Explanation:

Step1: Recall reflection rule

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

Step2: Identify polygon vertices

Let's assume the vertices of the triangle are $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$.

Step3: Apply reflection rule to vertices

For vertex $A(x_1,y_1)$, its image $A'(y_1,x_1)$; for $B(x_2,y_2)$, its image $B'(y_2,x_2)$; for $C(x_3,y_3)$, its image $C'(y_3,x_3)$.

Step4: Plot new - vertices

Plot the points $A'$, $B'$ and $C'$ on the coordinate - plane and connect them to form the reflected polygon.

Since we don't have the exact coordinates of $A$, $B$ and $C$ from the image, in general terms, if $A=(a,b)$, $B=(c,d)$, $C=(e,f)$:
The reflected points are $A'=(b,a)$, $B'=(d,c)$, $C'=(f,e)$. Plot these points to get the reflected polygon.

Answer:

Plot the points obtained by swapping the $x$ and $y$ coordinates of the original polygon's vertices and connect them to form the reflected polygon.