Transformation involves moving an object from its original position to a new position. The object in the new position is called the image. Each point in the object is mapped to another point in the image.

Example:

The original object is ABC and the image is A’B’C’. (A’ is read as A prime etc.)

In these lessons, we will study the following types of transformations in math:

Translation involves “sliding” the object from one position to another.

Reflection involves “flipping” the object over a line called the line of reflection.

Rotation involves “turning” the object about a point called the center of rotation.

Dilation involves a resizing of the object. It could result in an increase in size (enlargement) or a decrease in size (reduction).

Translation, reflection and rotations are called isometric transformations because the image is the same size and shape as the original object. The original object and the image are congruent.

Dilation is not an isometric transformation because the size of the image is not the same as the object. The original object and the image are similar i.e. they have the same shape but different size.

Videos - Translation

The following video shows an example of translation on the coordinate plane.

Translations GCSE foundation maths transformations translating shape using translation vectors

Videos - Reflection

The following video shows examples of math reflection across the y-axis and x-axis.

GCSE Maths transformations: Reflections made easy in horizontal and vertical lines

Videos - Rotation

The following video shows examples of math rotation about the origin (0, 0)

Rotations in the Coordinate Plane

Videos - Dilation

The following video shows examples of math dilation with different scale factors.

The following video shows enlargement by a positive and negative scale factor

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