Question

graph the image of the polygon after a reflection in the given line. (see examples 2 and 3.)

1. $y = x$
2. $y = -x$

Explanation:

Step1: Identify original points (13)

Points: $A(5, -3)$, $B(1, -2)$, $C(4, 1)$

Step2: Reflect over $y=x$ (swap $x,y$)

Reflected points:
$A'(-3, 5)$, $B'(-2, 1)$, $C'(1, 4)$

Step3: Identify original points (15)

Points: $A(-3, 2)$, $B(-4, 0)$, $C(-2, -2)$, $D(1, 0)$

Step4: Reflect over $y=-x$ ($(x,y)\to(-y,-x)$)

Reflected points:
$A'(-2, 3)$, $B'(0, 4)$, $C'(2, 2)$, $D'(0, -1)$

Answer:

For problem 13 (reflection over $y=x$):
Reflected triangle vertices: $A'(-3, 5)$, $B'(-2, 1)$, $C'(1, 4)$ (plot and connect these points to graph the image)
For problem 15 (reflection over $y=-x$):
Reflected quadrilateral vertices: $A'(-2, 3)$, $B'(0, 4)$, $C'(2, 2)$, $D'(0, -1)$ (plot and connect these points to graph the image)