How do you calculate the composition of two transformations?

The correct approach to calculating the composition of two transformations is to apply the first transformation to the original shape. Composition of transformations involves performing one transformation after another, where the order matters.

When you apply the first transformation, you take the original shape and modify it according to the rules of that transformation. The resulting shape then becomes the new shape onto which the second transformation will be applied. This sequential application is essential because it reflects how transformations impact geometric figures in succession.

For instance, if the first transformation is a translation to the right, and the second transformation is a rotation, the outcome will depend on how far the original shape has been translated before it is rotated. Following this systematic approach ensures that you accurately determine the final position and orientation of the shape after both transformations have been applied.

In contrast, reversing the order of transformations, applying the second transformation first, or averaging results do not accurately reflect how transformations combine in geometric contexts and can lead to incorrect outcomes. Understanding the proper sequence of applying transformations is crucial for correctly solving problems involving transformation compositions.