Translation Rules
Simply Explained w/ 5 Examples!

What are the translation rules?

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

Well, mathematically speaking, they’re the critical ingredients for isometric movements within a rigid body.

Now that may sound confusing at first, but that’s why we’re going to take this step-by-step in today’s geometry lesson.

So let’s get started!

A translation is sometimes referred to as a slide, shift, or glide as it maps (moves) all points of a figure the same distance and in the same direction.

In other words, imagine you put your right hand down on a flat surface. This is your preimage. Without changing the shape of your hand, you slide your hand along the surface to a new location. This is your image.

That’s all there is to translations… slide an object, without changing its shape, to a new location.

This means that a translation is an isometric transformation which means that the preimage and image are congruent figures, as ck-12 accurately states.

So how do we represent translations mathematically?

We use vectors to represent a translation. Which means we need direction (up, down, left, or right) and magnitude (length of units).

There are three ways we describe a translation:

1. Words
2. Coordinate Notation
3. Component Form of a Vector

As seen in the example below, we will learn how to take a preimage (triangle ABC) and translate it using vectors to find its image (triangle A’B’C’).

Translation Notation

In the following video, you’ll learn how to represent a translation, draw an interpretation given a transformation formula, and also discover how composite reflections can be represented as a translation.

Composition of Reflections Over Two Parallel Lines

Video – Lesson & Examples

38 min

• Introduction to translations
• 00:00:27 – What is a translation? How do we describe a translation? (Examples #1-2)
• Exclusive Content for Member’s Only

• 00:12:12 – Describe the translation in words, coordinate notation, and component vector form (Example #3)
• 00:20:56 – Graph the transformation given the translation rule (Example #4)
• 00:30:09 – How do two consecutive reflections equals one translation?
• 00:40:27 – Identify the following given consecutive reflections (Example #5)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions