Question

which graph shows δabc and its reflection across the y - axis, δabc?

Explanation:

To determine the correct graph, we use the rule for reflection across the \( y \)-axis: the \( x \)-coordinate of a point \((x,y)\) becomes \(-x\), while the \( y \)-coordinate remains the same. So, for \(\triangle ABC\) and its reflection \(\triangle A'B'C'\), corresponding points (e.g., \( A \) and \( A' \), \( B \) and \( B' \), \( C \) and \( C' \)) should be equidistant from the \( y \)-axis (mirror line) and have \( y \)-coordinates unchanged. The orange - colored graph (the third one) shows this property: the original triangle and its reflection across the \( y \)-axis have corresponding vertices symmetric with respect to the \( y \)-axis (same \( y \)-values, \( x \)-values are negatives of each other). The green graph does not show reflection (more like translation), and the purple graph shows reflection across the \( x \)-axis (since \( y \)-coordinates change sign).

Answer:

The graph in the orange - colored (third) option.