Question

Is it important to perform transformations in a specific order? The composition of the transformations that Jessie performed was in the order Translation, Reflection, Rotation. There are 5 other orders in which these transformations could be performed. Write two sets of instructions for another person to perform. The first set should describe a series of the transformations that gives the same result as the original, and the second set should describe a series that provides a different result.

Answer 1

Absolutely, the order in which transformations are performed is crucial because transformations are not always commutative, meaning that changing the order can lead to different final results.

**Set of Instructions for the Same Result (Translation, Reflection, Rotation):**

1. **Step 1: Translation**
- Move the object 5 units to the right.

2. **Step 2: Reflection**
- Reflect the object across the y-axis.

3. **Step 3: Rotation**
- Rotate the object 90 degrees clockwise around the origin.

**Set of Instructions for a Different Result (Rotation, Reflection, Translation):**

1. **Step 1: Rotation**
- Rotate the object 90 degrees clockwise around the origin.

2. **Step 2: Reflection**
- Reflect the object across the y-axis.

3. **Step 3: Translation**
- Move the object 5 units to the right.

These two sets of instructions illustrate how changing the order of transformations will yield different locations and orientations of the object in the plane.