Translations
A translation slides every point the same distance and direction.
About this topic
A translation slides every point of a figure the same distance in the same direction without turning or flipping. It is described by a vector or a rule such as (x, y) → (x + 3, y − 2). The image is congruent to the original and has the same orientation.
Translations are rigid motions, or isometries. They appear in wallpaper patterns, animation and computer graphics, where objects move across the screen.
Worked example: translate triangle with vertices A(1, 2), B(4, 2) and C(1, 5) by (x, y) → (x + 3, y − 2). The new vertices are A'(4, 0), B'(7, 0) and C'(4, 3). Every side keeps the same length and the figure faces the same way. Composing two translations, such as (+3, −2) then (−1, +4), gives one translation (+2, +2).
Video game characters moving across a screen, tiles in a pattern, and sliding doors all use translations. A frequent mistake is applying the rule to only some of the points, or moving the figure by the wrong sign. Read the vector carefully: positive x moves right and positive y moves up. Another is thinking that a translation changes size or orientation; it does not. Check by confirming that each vertex moved by exactly the same vector and that the shape looks identical.
Key ideas
- Described by a vector
- Shape and orientation stay the same
- Coordinates add the vector
Quick check
Use cases: where Translations helps
- Homework: review the key idea behind Translations before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Translations without notes.
- Visual learning: play with the interactive lab to see how Translations changes when you adjust its inputs.
- Teaching a friend: explain Translations 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 Translations?
A translation slides every point the same distance and direction.
What will I learn in Translations?
Described by a vector. Shape and orientation stay the same. Coordinates add the vector.
Is Translations 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 Translations 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 Translations?
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.