Question

triangle xyz was reflected across m and then dilated to form a similar triangle. which triangle represents the image?

Explanation:

Step1: Recall Reflection Properties

Reflection over line \( m \) should map points such that \( m \) is the perpendicular bisector of segments joining original and reflected points. Angles remain equal (congruent) after reflection.

Step2: Recall Dilation Properties

Dilation scales the figure (changes size) but keeps it similar (angles congruent, sides proportional). So the image after reflection and dilation should have the same angle measures as \( \triangle XYZ \) (due to reflection preserving angles, dilation preserving similarity) and be a scaled version.

Step3: Analyze Each Option

• First Option: The reflected triangle \( \triangle X'Y'Z' \) has angles that don't match (e.g., the single - arc and double - arc angles are misaligned in terms of correspondence after reflection and dilation).
• Second Option: After reflecting \( \triangle XYZ \) over \( m \), the angles (marked by arcs) should correspond, and then dilation (scaling) would keep the angle measures the same. The angle markings (single - arc at \( X' \), double - arc at \( Z' \)) match the original's angle markings (single - arc at \( X \), double - arc at \( Z \)) after reflection and dilation (since dilation preserves angle measures).
• Third Option: The reflection and dilation here do not preserve the angle - side correspondence correctly (the orientation and angle markings are inconsistent with the reflection - then - dilation process).

Answer:

The triangle in the middle (the second option among the three triangles shown)