Question

which graph shows △abc and △abc? the vertices of △abc are a(0,7), b(6,1), and c(0, - 6). graph △abc and △abc, its image after a reflection across the y - axis

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the y - axis, the transformation rule is $(x,y)\to(-x,y)$.

Step2: Apply rule to vertices

For point $A(0,7)$, after reflection across the y - axis, $A'(0,7)$ since $- 0=0$. For $B(6,1)$, $B'(-6,1)$. For $C(0, - 6)$, $C'(0,-6)$.

Step3: Identify correct graph

The graph that has $\triangle ABC$ with vertices $A(0,7),B(6,1),C(0, - 6)$ and $\triangle A'B'C'$ with vertices $A'(0,7),B'(-6,1),C'(0,-6)$ is the correct one. By visual inspection, we can see that the correct graph is the one where the triangle on one side of the y - axis is reflected to the other side maintaining the y - coordinates of the vertices and changing the sign of the x - coordinates of non - zero x - value vertices.

Answer:

We need to visually inspect the given graphs to find the one that shows $\triangle ABC$ with $A(0,7),B(6,1),C(0, - 6)$ and its y - axis reflection $\triangle A'B'C'$ with $A'(0,7),B'(-6,1),C'(0,-6)$. Without seeing all options clearly, we can't directly state which lettered option (A, B, C) is correct, but the process to find it is as described above. If we assume the graphs are labeled as in the problem statement and we have correctly identified the key points and the reflection rule, we look for the graph where the red and blue triangles are symmetric about the y - axis with the appropriate vertex coordinates.