How to Describe a Translation

Describing a Translation

A translation moves a shape. Every point of the shape is moved in the same direction by the same distance.

To describe a translation, we need to say in which direction and by what distance each point is moved.

Using a Column Vector to Describe a Translation

A column vector is used to describe a translation.

A column vector breaks down the translation into:

  • How far a shape moves in the horizontal direction (left or right).

  • How far a shape moves in the vertical direction (up or down).

An example of a column vector is shown below:

  • The top number (4) describes how the shape has moved in the horizontal direction.

    A positive number describes a move to the right.

    A negative number describes a move to the left.

  • The bottom number (2) describes how the shape has moved in the vertical direction.

    A positive number describes a move up.

    A negative number describes a move down.

How to Describe a Translation

Question

Describe the translation of the shape shown below.

The light blue shape is the original shape (called the object). The dark blue shape is the shape after it has been translated (called the image).

Step-by-Step:

Let us start by choosing a point on the object and see where it has been translated.

We will choose point A on the object. We see it has been translated to point A'.

1

Find how many units the point has moved in the horizontal direction. In our example, point A has moved 2 units to the right.

2

Write this as the top number in a column vector.

  • The point has moved 2 units, so the number will be 2.

  • The point has moved right, so the number will be positive.

3

Find how many units the point has moved in the vertical direction. In our example, point A has moved 2 units down.

4

Write this as the bottom number in a column vector.

  • The point has moved 2 units, so the number will be 2.

  • The point has moved down, so the number will be negative.

Answer:

The translation can be described by the column vector below:

Slider

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

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See Also

What is geometry? What are transformations? What is a positive number? What is a negative number?