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.

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Answered by GPT-4o mini
When triangle LMN is reflected across the y-axis to create triangle L'M'N', there are several key observations about the properties of the triangles:

1. **Corresponding Angles**: The measures of corresponding angles in triangle LMN and triangle L'M'N' will be equal. This is because reflection is a rigid transformation that preserves angle measures.

2. **Lengths of Corresponding Sides**: The lengths of corresponding sides in both triangles will also be the same. Again, this is a property of rigid transformations, which maintain distances.

3. **X-coordinates of Corresponding Vertices**: When a point (x, y) is reflected across the y-axis, its image becomes (-x, y). Hence, the x-coordinates of the corresponding vertices will have opposite signs. For example, if the vertices of triangle LMN are L(x₁, y₁), M(x₂, y₂), and N(x₃, y₃), then the vertices of triangle L'M'N' will be L'(-x₁, y₁), M'(-x₂, y₂), and N'(-x₃, y₃).

4. **Y-coordinates of Corresponding Vertices**: The y-coordinates of the corresponding vertices will remain unchanged during the reflection across the y-axis. So, if vertex L has coordinates (x₁, y₁), then vertex L' will have coordinates (-x₁, y₁).

In summary, reflecting triangle LMN across the y-axis results in triangle L'M'N' which has:

- Equal corresponding angles.
- Equal lengths of corresponding sides.
- X-coordinates that change sign.
- Y-coordinates that remain the same.

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