Definition
Dilation
A dilation scales every point's distance from one fixed centre by the same positive scale factor.
What it means
Picture a centre point with invisible rays through the shape. A dilation uses one multiplier on every ray. A factor greater than 1 makes the image larger; a factor between 0 and 1 makes it smaller; a factor of 1 leaves it unchanged. Because every distance uses the same factor, the shape is not stretched out of proportion.
Remember it
One centre, one multiplier: every point follows its ray and uses the same factor.
Example
Use centre O=(0,0) and scale factor 2. For triangle A(1,1), B(3,1), C(1,3), double both coordinates: A′(2,2), B′(6,2), C′(2,6). Every vertex is twice as far from O, every side length doubles, and the angles stay the same.
Watch for
Doubling only the width while keeping the height unchanged is not a dilation, because the distances are not all multiplied by the same factor.
Common mix-up
A dilation is not always an enlargement. A scale factor between 0 and 1 makes a reduction, and a scale factor of 1 leaves the figure unchanged.
Exact meaning
A dilation is a transformation with a fixed centre and a positive scale factor k. Each point moves along the ray from the centre through that point, and its distance from the centre becomes k times as large. Angle measures stay the same, and all lengths are multiplied by k.