Question

which graph shows the image of $\triangle abc$ after the glide reflection?
translation: $(x, y) \to (x + 2, y + 3)$
reflection: in the line $y = x$

Explanation:

Step1: Identify original coordinates

First, find coordinates of $\triangle ABC$ from the graphs:
$A=(-4, 2)$, $B=(-2, 3)$, $C=(0, 0)$

Step2: Apply translation rule

Use translation $(x,y)\to(x+2,y+3)$:
$A' = (-4+2, 2+3)=(-2,5)$
$B' = (-2+2, 3+3)=(0,6)$
$C' = (0+2, 0+3)=(2,3)$

Step3: Apply reflection over $y=x$

Reflection rule over $y=x$ is $(x,y)\to(y,x)$:
$A'' = (5,-2)$
$B'' = (6,0)$
$C'' = (3,2)$

Step4: Match to correct graph

Compare final coordinates to the options: these match the points in graph Option D.

Answer:

D. The graph with final image points $A''=(5,-2)$, $B''=(6,0)$, $C''=(3,2)$