In the previous posts, we have explored the fundamentals of translations and how to apply them to graphs and equations. Now, let's delve into the concept of composition of translations.

When we talk about composition, we're referring to combining two or more translations to create a single transformation. The order in which we apply the translations is crucial and affects the final position of the figure on the coordinate plane.

To create the composition of two translations, we need to perform them one after another. The resulting translation is equivalent to moving the figure once according to the first translation and then moving it again according to the second translation. This sequence of moves creates a completely new transformation.

For example, let's say we have a figure that is first translated 3 units to the right and then 2 units up. In this case, the composition of these two translations would be a new translation 3 units to the right and 2 units up from the original position of the figure.

It's important to note that the order of the translations does matter. If we reversed the order of the translations and first moved the figure 2 units up and then 3 units to the right, the final position of the figure would be different.

Practicing composition of translations will enhance your understanding of transformational geometry and allow you to confidently analyze complex figures on the coordinate plane. So grab your pencil, solve the practice problems, and let the transformations begin!