The Lesson

A translation moves a shape. Every point of the shape is moved in the same direction by the same distance. To translate a shape, we need to move each point in the shape in a certain direction by a certain distance. To simplify translating a shape, we break the translation down into:
  • How far we move the shape in a horizontal direction (left or right).
  • How far we move the shape in a vertical direction (up or down).

Using a Column Vector to Translate a Shape

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 in the horizontal direction (right if the number is positive, left if it is negative).
  • The bottom number (2) tells us how much to move the shape in the vertical direction (up if the number is positive, down if it is negative).

How to Translate a Shape

Translating a shape 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 top number in the column vector. In our example, the top number is 4.

2

The number found in Step 1 (4) will tell us how to move point A in the horizontal direction. If the number is positive, the point is moved right. If the number is negative, the point is moved left. In our example, 4 is positive. Move point A 4 units to the right.

3

Find the bottom number in the column vector. In our example, the bottom number is 2.

4

The number found in Step 3 (2) will tell us how to move the point in Step 2 in the vertical direction. If the number is positive, the point is moved up. If the number is negative, the point is moved down. In our example, 2 is positive. Move the point 2 units up.

Point A has been translated to to find A', the corresponding point on the translated shape. Repeat the Steps for Points B and C.

Answer:

Lesson Slides

The slider below shows another real example of how to translate a 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.

Top Tip

Stick to the Point!

When a shape is translated, each point in the shape moves the same direction and distance. When describing a translation, see how a single point has been moved. Choose a point on the shape, and see how it has moved after it has been translated.