Definition: A dilation is a transformation that enlarges or shrinks a figure by a scale factor from a fixed center, keeping its shape but changing its size.
What is a dilation?
It stretches or shrinks a figure from a center point. Every distance from the center is multiplied by the scale factor k.
How does k change things?
- k > 1: enlargement
- 0 < k < 1: reduction
- k = 1: no change
How do you use coordinates?
With the center at the origin, (x, y) becomes (kx, ky). Dilate triangle A(2, 4), B(6, 4), C(2, 10) by k = 1/2: A'(1, 2), B'(3, 2), C'(1, 5).
What stays and what changes?
Angles stay the same and sides stay proportional, but lengths change by k. The image is similar to the original, not congruent unless k = 1. A side of 6 becomes 3, and area is multiplied by k squared, here 1/4.
How do you find k from two figures?
Compare matching lengths: new length divided by original. A segment from 8 to 20 gives k = 20 / 8 = 2.5.
What is a common mistake?
Thinking a dilation moves the figure only. It also resizes it. Another slip is to mix up image and preimage when computing k.
Where to learn it
- Moving Shapes with Translations, Reflections, Rotations – lesson
- Congruent and Similar Figures Through Dilations – lesson