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Translation (Mathematics Lesson)

What Is a Translation?

In geometry, a translation moves a shape without rotating, reflecting or resizing it.

Each point on the shape moves the same direction and distance.

A translation is a type of transformation.

A Real Example of Translation



The diagram above shows a triangle before (light blue) and after (dark blue) being translated.

The triangle has been moved, but has not been rotated, reflected nor resized. Each point on the triangle has been moved by the same direction and distance (shown by the arrow).

Describing a Translation

Question: Describe the translation below.



A translation is described by how each point has moved in the co-ordinate plane.

Each point has moved 2 squares to the right and 3 squares up.

This is best described using a column vector:



Read more about how to descibe a translation

How to Translate a Shape

Question: Translate the shape below by
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Each point on the shape is translated according to the column vector:

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Point A is translated to point A'.

Point B is translated to point B'.

Read more about how to translate a shape
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Note

TRANSFORMATIONS

A translation is a type of transformation.

The other types of transformation are:

TRANSLATED SHAPES ARE CONGRUENT SHAPES

If a shape can be transformed to another using only translation, then the two shapes are congruent.

Congruent shapes have the same size, line lengths, angles and areas.

They are the same shape and size, just in a different position.

COLUMN VECTORS

Translations are best described using column vectors.

The column vector describes the change in the shape's position in the horizontal and vertical direction:

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  • The x value tells you how many units in the horizontal direction the shape has moved.

    A positive value means it has moved right.
    A negative value means it has moved left.

  • The y value tells you how many units in the vertical direction the shape has moved.

    A positive value means it has moved up.
    A negative value means it has moved down.

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