Dilations
Scale a figure from a centre by factor k.
Key idea
Scale a figure from a centre by factor k.
In depth
A dilation scales distances from a centre by a factor k. Shape is preserved but size changes by k; if k < 1 it shrinks, and a negative k also flips it through the centre. It produces similar figures.
Worked example
Dilating (2, 3) by k = 3 about the origin → (6, 9). Lengths ×3, area ×9.
Formula
Real-world uses
- Zooming a map or a photo
- Scaling a design up for printing or down for a website icon
Common mistake
Scaling area by k rather than k².
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Dilations?
Scale a figure from a centre by factor k. It is a topic at the intermediate level in Geometry.
What is the formula for Dilations?
The key formula is (x,y) → (kx, ky).
Where is Dilations used in real life?
Real-world examples: Zooming a map or a photo; Scaling a design up for printing or down for a website icon.
What should I learn before Dilations?
Make sure you are comfortable with Rotations, the previous topic in Geometry.
What is a common mistake with Dilations?
Scaling area by k rather than k².
How can I practise Dilations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Dilations?
Move on to Symmetry next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.