Question

challenge the vertices of △abc are a(-4,4), b(-2,3), and c(-3,2). △abc is reflected across the y - axis and then reflected across the x - axis to produce the image △abc. graph △abc and △abc. which graph shows △abc and △abc?

Explanation:

Step1: Recall reflection rules

Reflection across y - axis: $(x,y)\to(-x,y)$.
For $A(-4,4)$: $A'=(4,4)$; for $B(-2,3)$: $B'=(2,3)$; for $C(-3,2)$: $C'=(3,2)$.

Step2: Apply reflection across x - axis

Reflection across x - axis: $(x,y)\to(x, - y)$.
For $A'(4,4)$: $A''=(4,-4)$; for $B'(2,3)$: $B''=(2,-3)$; for $C'(3,2)$: $C''=(3,-2)$.

Step3: Analyze graphs

Check which graph has $\triangle ABC$ with vertices $A(-4,4),B(-2,3),C(-3,2)$ and $\triangle A''B''C''$ with vertices $A''(4,-4),B''(2,-3),C''(3,-2)$.

Answer:

(Without seeing the actual options clearly, we can't give a specific letter - option. But the above steps show how to determine the correct graph. If we assume we have analyzed the graphs based on the above - calculated coordinates, we would pick the graph that has the correct pre - image and final image triangles.)