Dilations
A dilation resizes a figure by a scale factor from a center.
About this topic
A dilation enlarges or shrinks a figure from a centre point by a scale factor k. Every point moves so that its distance from the centre is multiplied by k. If k greater than 1 the image grows, if 0 less than k less than 1 it shrinks, and the image is similar to the original: same shape, different size.
Lengths scale by k and areas by k². Dilations are used in maps, photo enlargements, model building and zooming on screens, and are the transformation behind similarity.
Worked example: dilate triangle A(2, 2), B(6, 2), C(2, 4) from the origin with k = 2 to get A'(4, 4), B'(12, 4), C'(4, 8). Side AB of length 4 becomes 8, and the area grows from 4 to 16. With k = 1/2 the figure shrinks to half size, and a negative k also flips it through the centre.
A photocopier set to 150 percent, the zoom on a phone, and a scale drawing of a house are dilations. People often think area doubles when lengths double, but it multiplies by k squared; volumes scale by k cubed. A frequent error is adding k to coordinates when it should multiply them. If the centre is not the origin, find the vector from the centre to each point and scale it. Remember that a dilation with k = 1 changes nothing and that angles stay the same.
Key ideas
- k > 1 enlarges, 0 < k < 1 shrinks
- Angles stay equal
- Lengths scale by k and areas by k²
Quick check
Use cases: where Dilations helps
- Homework: review the key idea behind Dilations before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Dilations without notes.
- Visual learning: play with the interactive lab to see how Dilations changes when you adjust its inputs.
- Teaching a friend: explain Dilations in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Dilations?
A dilation resizes a figure by a scale factor from a center.
What will I learn in Dilations?
k > 1 enlarges, 0 < k < 1 shrinks. Angles stay equal. Lengths scale by k and areas by k².
Is Dilations part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Dilations lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Dilations?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.