What Is Dilation?

Dilation

A transformation that changes the size of a figure without changing its shape. The figure is enlarged or reduced from a fixed point called the centre of dilation.

Imagine you're zooming in or out on a photo on your phone. The image gets bigger or smaller, but everything in the photo keeps the same proportions — people don't suddenly become taller and thinner! That's exactly what dilation does in geometry.

Analogy

Think of a projector shining an image onto a screen. The projector lens acts like the centre of dilation. If you move the projector closer to the screen, the image shrinks. If you move it farther away, the image grows. How much the image grows or shrinks is described by the dilation factor.

Key features of a dilation:

The shape of the figure stays the same (angles don't change)
The size of the figure changes
The original figure and the dilated figure are similar
Every point moves along a straight line from the centre of dilation

Note

Connection to Science: Dilation is the mathematical foundation behind many real-world scientific tools. A microscope magnifies a specimen — enlarging it by a dilation factor so you can see details invisible to the naked eye. A scale model of a cell or a molecule is a reduction dilation. You'll see dilation at work wherever scientists need to represent objects at a different size while keeping their true proportions.

The Dilation Factor (Scale Factor)

Dilation Factor (Scale Factor)

The ratio that describes how much a figure is enlarged or reduced during a dilation. It is usually represented by the letter k.

The dilation factor k tells you the relationship between the new (image) figure and the original (pre-image) figure:

$k = \frac{length on image}{corresponding length on pre-image}$

What the value of k tells you:

If $k > 1$ : the figure is enlarged (gets bigger)
If $0 < k < 1$ : the figure is reduced (gets smaller)
If $k = 1$ : the figure stays the same size (no change)

Exam Tip

A quick way to remember: if k is a whole number greater than 1, the shape grows. If k is a fraction between 0 and 1, the shape shrinks.

Note

Extension note: In more advanced mathematics, you may encounter a negative scale factor ( $k < 0$ ). This produces an image on the opposite side of the centre of dilation — the figure is both scaled and rotated 180° around the centre. This is beyond what we cover at MYP 3, but worth knowing exists!

Free preview

9 more sections in this topic

Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.