There are two types of transformations:

Some transformations, such as translations, rotations, and reflections involve moving a shape so that it is in a different position, but still has the same size, area, angles, and line lengths.

A dilation is a transformation in which the size, area, angles, and line lengths change.

Translation

Translations move a shape, without rotating or flipping the shape. The shape slides in a given direction.

The shape still looks exactly the same; it is just in a different place.

A translation relocates a figure with additional informration about the direction and distance of the translation.

The following figure is translated up and to the left.

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Rotation

A rotation is a transformation in which a figure is turned about a given point.

The center of rotation is the fixed point around which a two-dimensional figure is rotated.

Here are two examples of rotation.

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Reflection

A reflection is an image or shape as it would be seen in a mirror.

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Dilation

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure.

The description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. It is the only point that remains unchanged under a dilation.

A dilation can enlarge or reduce a shape by a given scale factor. A good example is when you make a copy on a copy machine. We can reduce or enlarge the original by a scale factor given as a percentage, e.g. 200% or 50%.

Note that the heart shape below remains in the shape of a heart as it enlarges.

Shapes can be dilated by a scale factor.

If we dilate by a scale factor of 25% (on the left) versus a scale factor of 150% (on the right), how will our images differ in size to the original (in the middle)?

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Connecting the Concepts

Transformations

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