Question

Xavier reflects triangle LMN across the y-axis to create its image triangle L'M'N'. Xavier then compares the measures of corresponding angles, the lengths of corresponding sides, the x-coordinates of corresponding vertices, and the y-coordinates of corresponding vertices in the two figures.

Which of the aspects bolded above were NOT the same in the two triangles?

Answer 1

When triangle LMN is reflected across the y-axis to create triangle L'M'N', the following aspects are affected:

1. **Measures of corresponding angles:** These will remain the same because reflections preserve angle measures. Thus, the angles of triangle L'M'N' will be equal to the angles of triangle LMN.

2. **Lengths of corresponding sides:** The lengths of the sides will also remain the same because reflections preserve distances. Therefore, the side lengths of triangle L'M'N' will be equal to those of triangle LMN.

3. **x-coordinates of corresponding vertices:** The x-coordinates will change. For a reflection across the y-axis, the x-coordinate of each vertex will be negated. For example, if vertex L has coordinates (x, y), after reflection, L' will have coordinates (-x, y). This means the x-coordinates of corresponding vertices will NOT be the same.

4. **y-coordinates of corresponding vertices:** The y-coordinates will remain the same because the reflection does not affect the vertical position of the points. If vertex L has coordinates (x, y), then L' will have coordinates (-x, y). Therefore, the y-coordinates of corresponding vertices will be the same.

In summary, the aspects that were NOT the same in the two triangles are the **x-coordinates of corresponding vertices**. All other aspects—angle measures and lengths of corresponding sides—remain the same.