Understanding Dilation in Geometry: Enlargement and Reduction Explained.

Dilation

An enlargement or reduction of a figure

Dilation is a geometric transformation that changes the size of a figure, but not its shape. Dilation is often referred to as scaling or enlargement. When a figure is dilated, all of its points are moved an equal distance away from a fixed point known as the center of dilation. The size of the dilation is determined by a scale factor which is a positive real number. If the scale factor is greater than one, the dilation is an enlargement, which means the figure gets larger. If the scale factor is less than one, the dilation is a reduction, which means the figure gets smaller.

To perform a dilation, the following steps can be taken:

1. Determine the center of dilation.
2. Determine the scale factor.
3. For each point of the figure, find the distance between the center of dilation and the point.
4. Multiply the distance by the scale factor.
5. Using the product from step 4 as the new distance, draw a new point on the same line between the center of dilation and the original point.

It is important to note that a dilation preserves angles, but not necessarily lengths or areas. In other words, the angles of the original figure and the dilated figure will be congruent, but the sides and perimeter of the new figure will change proportionally to the scale factor.

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