# 8.18: Transformation Classification

**At Grade**Created by: CK-12

**Practice**Transformation Classification

Mrs. Gilcrest has designed a special version of the game Battleship. Her version requires students to use coordinates such as (1, 2) to guess the location of a ship. The ships are strategically placed so that each is a translation of the other. In order to keep the game easier for the students, she translated the ships the same distance up or down, right or left. If the first ship is at (3, 6), (3, 7), (3, 8) and the second ship is translated 4 units to the right and 4 units up, what are the coordinates of the second ship?

In this concept, you will learn how to classify transformations.

### Classifying Transformations

The **coordinate plane** is a representation of two-dimensional space. It has a **horizontal axis**, called the **vertical axis**, called the

Remember the three types of transformations: translation, reflection and rotation.

Now let’s look at performing each type of transformation in the coordinate plane.

When you perform translations, you slide a figure left or right, up or down. This means that on the coordinate plane, the coordinates for the vertices of the figure will change. Take a look at the example below.

Now let’s look at performing a translation or slide of this figure.

You can choose the number places that you want to move the triangle and the direction that you wish to move it in. If you slide this triangle 3 places down, all of its vertices will shift 3 places down the

Let’s see why this happens.

You can see the change in all of the

You can translate figures in other ways, too. As you might guess, you move figures right or left on the coordinate grid by their

Here is an example of how to graph a translation.

Slide the following figure 5 places to the right.

In this translation, you will move the figure to the right. That means the

Once you relocate each point 5 places to the right, you can connect them to make the new figure that shows the translation.

You can check to see if you performed the translation correctly by adding 5 to each **coordinate notation**. Notice that each point is represented by coordinates.

These are the points you graphed, so you have performed the translation correctly.

### Examples

#### Example 1

Earlier, you were given a problem about Mrs. Gilcrest and her special version of the game Battleship.

She translated the ships the same distance up or down, right or left. If the first ship is at (3, 6), (3, 7), (3, 8) and the second ship is translated 4 units to the right and 4 units up, what are the coordinates of the second ship?

First, remember the signs associated with a move to the right and a move up.

Right is a move in the positive direction on the

Next, add the moves to the coordinates.

(3+4, 6+4), (3+4, 7+4), (3+4, 8+4)

Then write the new vertices

(7, 10), (7, 11), (7, 12)

The coordinates of the second ship are (7, 10), (7, 11), (7, 12).

#### Example 2

Solve this problem.

Slide the following figure 4 places to the left and 2 places up.

First, graph the new points.

Graph each point by counting 4 places to the left, and from there 2 places up.

Then, form the new triangle.

Connect the new points.

You can check the translation by changing the

#### Example 3

Translate triangle

First, remember whether up is a move on the

Up is a move on the

Next, add 4 to each of the

(0, 1+4), (1, 3+4), (4, 0+4)

Then, write the new vertices.

(0, 5), (1, 7), (4, 4)

The new triangle has coordinates (0, 5), (1, 7), (4, 4).

#### Example 4

Translate triangle

First, remember whether down is a move on the

Down is a move on the

Next, subtract 2 from each of the

(-3, 2-2), (1, 6-2), (2, 1-2)

Then, write the new vertices.

(-3, 0), (1, 4), (2, -1)

The new triangle has coordinates (-3, 0), (1, 4), (2, -1)

#### Example 5

Translate triangle

First, remember whether right is a move on the

Right is a move on the

Next, add 3 to each

(-5+3, 4), (1+3, 8), (3+3, 5)

Then write the new vertices

(-2, 4), (4, 8), (6, 5)

The new triangle has coordinates (-2, 4), (4, 8), (6, 5).

### Review

Identify the transformations shown below as a translation, reflection, or rotation.

- True or false. This figure has been translated 5 places to the right.

Translate each figure to the right 6 places and up 1. Then write the new coordinates for the figure.

- Triangle
DEF (-1, 2)(1, 6)(2, 1) - Triangle
DEF (-3, 2)(1, 6)(2, 1) - Triangle
DEF (0, 2)(1, 6)(2, 1) - Triangle
DEF (4, -2)(1, 6)(2, 1) - Triangle
DEF (5, 3)(1, 6)(2, 1) - Triangle \begin{align*}DEF\end{align*} (4, 4)(1, 6)(2, 1)

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.18.

### Resources

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

Please Sign In to create your own Highlights / Notes | |||

Show More |

axis

The axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.axis

The axis is the vertical number line of the Cartesian plane.Coordinate Plane

The coordinate plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate plane is also called a Cartesian Plane.Transformation

A transformation moves a figure in some way on the coordinate plane.### Image Attributions

In this concept, you will learn how to classify transformations.

## Concept Nodes:

**Save or share your relevant files like activites, homework and worksheet.**

To add resources, you must be the owner of the Modality. Click Customize to make your own copy.