Question

does the graph show a reflection of triangle abc? image of coordinate plane with triangles abc and abc options: no, the graph is not a reflection. yes, the graph reflects over the y - axis. yes, the graph reflects over the x - axis.

Explanation:

Step1: Recall reflection rules

A reflection over the \(x -\)axis changes the \(y -\)coordinate of a point \((x,y)\) to \((x, - y)\). A reflection over the \(y -\)axis changes the \(x -\)coordinate of a point \((x,y)\) to \((-x,y)\).

Step2: Analyze the orientation

If we consider the positions of the triangles. If it were a reflection over the \(y -\)axis, the left - right orientation would be reversed with respect to the \(y -\)axis. If it were a reflection over the \(x -\)axis, the up - down orientation would be reversed with respect to the \(x -\)axis.
Looking at the given graph, the two triangles are not symmetric with respect to the \(x -\)axis (since the \(y -\)coordinate relationship for corresponding vertices does not follow \(y\to - y\)) and not symmetric with respect to the \(y -\)axis (since the \(x -\)coordinate relationship for corresponding vertices does not follow \(x\to - x\)).

Answer:

No, the graph is not a reflection.