Pilar draws rectangle JKLM in the coordinate plane. She preforms two transformations on rectangle JKLM to form rectangle J"K"L"M. What two transformations could Pilar have used?

To determine the two transformations Pilar could have used to transform rectangle JKLM into rectangle J"K"L"M, let's consider common transformations in the coordinate plane:

1. **Translation** – This transformation slides the rectangle without changing its size or orientation. Each point is moved by the same distance in a given direction.
2. **Reflection** – This flips the rectangle across a line, such as the x-axis, y-axis, or any other line of reflection.
3. **Rotation** – This rotates the rectangle around a specific point, usually the origin or a corner of the rectangle, by a certain angle (e.g., 90°, 180°, etc.).
4. **Dilation** – This changes the size of the rectangle by a certain scale factor while maintaining its shape. A dilation either enlarges or shrinks the rectangle.

Two transformations Pilar could have used:
- **Reflection followed by a Translation**: This would flip the rectangle across a line (like the x-axis) and then move it to a different position.
- **Rotation followed by a Translation**: This would rotate the rectangle by a certain angle (like 90° or 180°) and then move it to another location.

### Do you want specific coordinates for examples, or further explanation on how each transformation works?

Here are 5 relative questions to think about:
1. How does the reflection across the x-axis change the coordinates of a rectangle?
2. What would happen if Pilar reflected the rectangle across the y-axis instead?
3. How does rotation by 180° affect the orientation of the rectangle?
4. Can a dilation result in a rectangle of the same size as the original?
5. How does a translation transformation preserve the shape and size of a rectangle?

**Tip**: When performing transformations, always track how each vertex (corner) of the shape changes in coordinates. This helps visualize the overall transformation.

Pilar draws rectangle JKLM in the coordinate plane. She performs two transformations on rectangle JKLM to form rectangle J"K"L"M. What two transformations could Pilar have used?

Explore how Pilar performs two transformations on rectangle JKLM in the coordinate plane to form rectangle J"K"L"M. Learn about translation, reflection, and rotation transformations, including their effects on coordinates. Suitable for students in Grades 6-8.

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