Question

∆ABC was transformed according to the rule (x, y) → (−x, y) to create ∆A'B'C'. What transformation justifies the relationship between the triangles? A translation 1 unit to the left and 1 unit upward justifies ∆ABC ~ ∆A'B'C'. A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'. A rotation of 90° clockwise justifies ∆ABC ~ ∆A'B'C'. A rotation of 90° counterclockwise justifies ∆ABC ≅ ∆A'B'C'.

Answer 1

A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'. The given rule (x, y) → (−x, y) corresponds to a reflection over the y-axis, where the x-coordinates are negated while the y-coordinates remain unchanged. This transformation is consistent with the relationship between ∆ABC and ∆A'B'C'.

Answer 2

A reflection over the y-axis

Explanation:

Because we can see the x-coordinate changes, and nothing else, we can assume that the shape is either being translated horizontally, or being reflected across the x-axis. We can see that the x-coordinate is turned to a negative, so it is reflected.