# Translations

- Author:
- Shannon Rush

A translation is a transformation that creates a new figure through "sliding."
After any transformation, the new shape created is called the Image. The points of the image are named with the corresponding letter to the original figure, but with an apostrophe. For example, the image of point A, is A'. We read this notation "A prime."
Click the box labeled "Translation" in the GeoGebra sketch below to show the translated the triangle. Notice how the points of the image are named.
The black ray is the vector that creates the movement.
+ Manipulate the points of the triangle and observe what happens to the points, segments, and angle measures.
+ Manipulate the vector length and angle and observe what happens to the points, segments, and angle measures.

## What are the effects of translations on the points, segments and angle measurements?

Summarize your understanding of the relationship between the points, segment lengths, and angle measures of the original figure and its image after a translation.

## Vector Components

Each vector can be divided into horizontal and vertical components. The horizontal component is represented by h. The vertical component is represented by k.
Click on the components box below and observe the relationship between the components of the vector and the location of the image.

## H -- Horizontal Component

How does the horizontal component of the vector affect location of the image?

## K -- Vertical Component

How does the vertical component of the vector affect location of the image?

One can express the translation at a rule that changes each point. The translation rule is written.

Given the rule , describe how the original object would be moved to create the image.

What translation was used to create the image above?

Now, return to the GeoGebra sketch. Add lines connecting the original point to its image. Record your observations in the box below the sketch.

What did you observe about the lines connecting the original points to their image? Justify your reasoning.

## Can you do it on your own?

Create a vector using the "Vector" tool. Then, use the "Translate by Vector" tool to translate the triangle by selecting the triangle and the vector you've created.

## Challenge!

Return to the sketch above. Add a second vector using the "vector" tool (third button). Use the "translate by a vector" tool (fourth button) to translate the image by selecting the image and your new vector.
The combination of more than one transformation applied to an object it is called a composition.
Record the summary of your observations below.

Observations of the effects of a composition of two translations.