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.