What Is a Dilation Calculator?
A dilation calculator finds the new position of a point or shape after a dilation — a transformation that enlarges or shrinks a figure by a scale factor about a fixed center point. Dilations preserve shape but change size, and they are a key topic in geometry. Enter the point's coordinates, the center of dilation, and the scale factor, and the calculator returns the dilated coordinates.
How to Use the Calculator
- Enter the original point coordinates (x, y).
- Enter the center of dilation (often the origin).
- Enter the scale factor.
- Calculate — see the new coordinates.
The Dilation Formula
For a dilation about the origin with scale factor k, each coordinate is multiplied by k:
(x, y) → (kx, ky)
For a center (a, b), the formula is (a + k(x − a), b + k(y − b)), which moves each point along the line from the center, scaled by k.
What the Scale Factor Does
| Scale Factor k | Effect |
|---|---|
| k > 1 | Enlargement (figure grows) |
| k = 1 | No change |
| 0 < k < 1 | Reduction (figure shrinks) |
| k < 0 | Enlargement/reduction with a 180° flip |
Properties of Dilations
- Shape preserved: the image is similar to the original.
- Angles unchanged: corresponding angles stay equal.
- Lengths scaled: every length is multiplied by |k|.
- Center fixed: the center of dilation does not move.
Frequently Asked Questions
What is a dilation in geometry?
A dilation is a transformation that enlarges or shrinks a figure by a scale factor about a fixed center, preserving shape but changing size.
How do you dilate a point?
For a dilation about the origin, multiply both coordinates by the scale factor: (x, y) becomes (kx, ky). For other centers, scale the distance from the center.
What does the scale factor do?
A scale factor greater than 1 enlarges the figure, between 0 and 1 shrinks it, and a negative factor also flips it 180° about the center.
Does dilation change angles?
No — dilations preserve angles and overall shape, so the image is similar to the original; only the size changes.
Is this dilation calculator free?
Yes — it is completely free, requires no signup, and finds dilated coordinates.