The vertices of triangle A'B'C' resulting from reflecting triangle ABC across the line x = 1 are A' (1, 4), B' (-2, 2), and C' (-1, 5). The perpendicular bisector property confirms the reflection.
The triangle resulting from reflecting triangle ABC across the line x = 1 is triangle A'B'C'. The vertices of A'B'C' are A' (1, 4), B' (-2, 2), and C' (-1, 5).
The reflection of a point across a vertical line involves changing the sign of its x-coordinate while keeping the y-coordinate unchanged. Accordingly, A' is the reflection of A with coordinates (2, 4), resulting in A' (1, 4). Similarly, B' is the reflection of B with coordinates (4, 2), yielding B' (-2, 2). Lastly, C' is the reflection of C with coordinates (0, 5), giving C' (-1, 5).
The perpendicular bisector property of reflections indicates that each side of triangle A'B'C' is bisected by the line x = 1. This geometric relationship supports the conclusion that triangle A'B'C' is indeed the reflection of triangle ABC across the line x = 1.