Question

compositions a composition of transformations maps △xyz to △xyz. the first transformation for this composition is ____, and the second transformation is a 90° rotation about point x. options: a translation to the right, a reflection across line m, a 180° rotation about point x, a 270° rotation about point x.

Explanation:

To determine the first transformation, we analyze the position of \( \triangle XYZ \) and \( \triangle X'Y'Z' \). A reflection across line \( m \) would map the original triangle to the position of \( \triangle X'Y'Z' \) as the orientation and distance from line \( m \) match the reflection property. Other options like translation or rotation about \( X \) don't align with the visual transformation from \( \triangle XYZ \) to \( \triangle X'Y'Z' \) as well as reflection across \( m \).

Answer:

a reflection across line \( m \)