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.