Lesson 24 — Activity 1: Translations

Getting Ready

Have you ever been to an amusement park with a variety of exciting rides? Rides there are certainly examples of objects (and people) in motion.

Transformations are movements of objects from one place to another place. This is also called motion geometry.

In the activities for this lesson, you will look at three transformations:

slides — translations
flips — reflections
turns — rotations

This first activity is about translations.

A roller coaster is certainly an example of objects in motion.
Image courtesy of www.imagesgoogle.com

The roller coaster in the above image is an example of a translation (slide). During a translation, an object has remained aligned in the same direction and has moved, or slid, to another spot. When you learned about moving shapes from one location on a grid to another in L23 — A2, you learned about translation.

Let's look more closely at this kind of transformation. Here's an example:

 You will see how this triangle can be moved.

Do you notice that all of the points in the image above have letters attached to them? This allows you to verbally describe the picture as well as allows you to compare your new coordinates with your old ones.

New coordinates will be shown with a prime ( ' ) symbol beside them. This shows that they are a different version of the original coordinates.

Say you want to translate the above triangle 4 units to the right. You would add 4 to all the x coordinates.

(3 + 4,8) = (7,8) A' 

(4 + 4,4) = (8,4) B' 

(1+ 4,5) = (5,5) C'

Your translated coordinates are A' (7,8), B' (8,4), and C' (5,5), and the translated picture would look like this:

You can see how the triangle has been moved.

Digging Deeper

Click here to see two more examples of translations of shapes. The first page shows the original images, and the second page shows where the shapes are placed after the translations.