Question

graph the polygon with the given vertices and its image after a reflection in the line y = x. a(0, - 3), b(2, 2), c(5, 0)

Explanation:

Step1: Recall reflection rule

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

Step2: Reflect point A

For point A$(0,- 3)$, after reflection in $y = x$, the new - point A' is $(-3,0)$.

Step3: Reflect point B

For point B$(2,2)$, after reflection in $y = x$, the new - point B' is $(2,2)$ (since $x = y$ for this point).

Step4: Reflect point C

For point C$(5,0)$, after reflection in $y = x$, the new - point C' is $(0,5)$.

Step5: Graph the original and reflected polygons

Plot the original points A$(0,-3)$, B$(2,2)$, C$(5,0)$ and connect them to form the original polygon. Then plot the reflected points A'$(-3,0)$, B'$(2,2)$, C'$(0,5)$ and connect them to form the reflected polygon.

Answer:

The original polygon has vertices A$(0,-3)$, B$(2,2)$, C$(5,0)$. The reflected polygon in the line $y = x$ has vertices A'$(-3,0)$, B'$(2,2)$, C'$(0,5)$.