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In Geometry, transformation means changing the appearance of an object. There are many ways in which this can be done. In this section we cover the most basic method of transformation that is Translation of Shape.

Definition

The term Translation is used in Geometry for a function that moves an object by a certain distance. However it is important to note that the object is only moved and not altered by any other means such as reflection, rotation or resizing.

As is evident from the definition of translation of shape, since the object is not altered in any other way, this implies that every point on the object must be moved in the same way - that is in the same direction and also by the same distance.

Terms related to translation of shape

Let us understand some of the terms that are frequently used along with the translation function:

Preimage - this term is used to refer to the original object
Image - this term is used to refer to the object after it has been translated.

Usually an arrow is used to indicate the direction in which the object has moved. This arrow also helps us to identify the image and the preimage clearly.

Properties of a translation

The original object and the translated object are identical in every way except for their position. This is also referred to as congruence.

If we draw line segments linking a vertex in the original object to the corresponding vertex in the translated object, these segments will be parallel and congruent.

Translation math examples

For translation maths tests, different types of translation problems can be presented. In one approach you are shown a figure on a coordinate plane that has to be translated. The required translation has to be defined in terms of the distance and also the direction of the transformation to be performed.

For example you could be asked to translate a simple right angled triangle down five units.

In order to solve this problem, you will take each vertex point of the triangle and move it down by 5 units on the given plane. Thus a point (1,5) should move to (1,0).

Note: this example only asked us to translate the shape along the y axis.

Another example is to translate the same triangle down by 5 units and right by 3 units.

Now not only do you need to count down by 5 units, you also need to count right by 3 units on the plane that is along both x and y axis. Hence a point at (1,5) will now be at (4,0) in the translated image.

All the vertices in the triangle should move in this fashion.

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