## Using Cartesian Coordinates to Translate a Shape

Cartesian coordinates can be used to translate a shape.## Cartesian Coordinates Tell You Where a Point Is

Cartesian coordinates are used to describe the position of a point on a graph. They consist of a pair of coordinates:- The x-coordinate tells us how far
**across**a point is. - The y-coordinate tells us how far
**up**a point is.

**1**and the y-coordinate of the point is

**2**. The Cartesian coordinates are

**(1, 2)**.

## A Column Vector Tells You How to Move Each Point

A column vector tells us how to translate a shape. A column vector shows two numbers, one above the other. An example of a column vector is shown below:- The top number (4) tells us how much to move the shape
**across**. - The bottom number (2) tells us how much to move the shape
**up**.

## Using the Column Vector to Find the Cartesian Coordinates of the Translated Shape

The numbers in the column vector are added to the Cartesian coordinates of the point.- The top number of the column vector is added to the x-coordinate of the point.
The image below shows the top number of the column vector (4) being added to the x-coordinate of the point (1):

The point on the translated shape is 5 (= 1 + 4) - The bottom number of the column vector is added to the y-coordinate of the point.
The image below shows the bottom number of the column vector (2) being added to the y-coordinate of the point (2):

The point on the translated shape is 4 (= 2 + 2)

**(5, 4)**.

## How to Translate a Shape Using Cartesian Coordinates

Translating a shape using Cartesian coordinates is easy.## Question

Translate the shape below using the column vector.## Step-by-Step:

Let us start by choosing a point on the shape and translating it. We will translate point**A**.

## 1

Find the Cartesian coordinates of the point.

In our example, the Cartesian coordinates the point

In our example, the Cartesian coordinates the point

**A**is**(1, 3)**.## 2

Add the top number of the column vector (4) to the x-coordinate of the point (1).

1 + 4 = 5

The x-coordinate of the translated point is **5**.## 3

Add the bottom number of the column vector (2) to the y-coordinate of the point (3).

3 + 2 = 5

The y-coordinate of the translated point is **5**.## 4

Draw the translated point at with the x-coordinate found in

Point

**Step 2**(5) and the y-coordinate found at**Step 3**(5). The translated point has Cartesian coordinates of**(5, 5)**.Point

**A**has been translated to to find**A'**, the corresponding point on the translated shape.**Steps**for Points

**B**and

**C**. It can be easier to translate each point in a table:

- Column
**(1)**has the x-coordinate of each point. - Column
**(2)**has the y-coordinate of each point. - Column
**(3)**adds the top number in the column vector (4) to the number in column**(1)**. - Column
**(4)**adds the bottom number in the column vector (2) to the number in column**(2)**.

(1) | (2) | (3) = (1) + 4 | (4) = (2) + 2 | ||
---|---|---|---|---|---|

Point | X-Coordinate | Y-Coordinate | Translated X-Coordinate | Translated Y-Coordinate | Point |

A | 1 | 3 | 5 | 5 | A' |

B | 1 | 2 | 5 | 4 | B' |

C | 2 | 2 | 6 | 4 | C' |

## Answer:

We have translated the shape.## What Is a Translation?

A translation is a slide of a shape: without rotating, reflecting or resizing it. A translation is a type of transformation.## You might also like...

graphs and coordinate geometryfinding the midpoint between pointsreflecting shapes in the x-axisreflecting shapes in the y-axis

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.