Translations
Slide a figure by a vector.
Key idea
Slide a figure by a vector.
In depth
A translation slides every point the same distance in the same direction, described by a vector. Shape, size and orientation are unchanged, so it is a congruence transformation.
Worked example
Translating (2, 3) by (4, −1) gives (6, 2).
Formula
Real-world uses
- Sliding tiles in a game
- Moving a sprite across a screen
- Shifting a pattern along a border
Common mistake
Changing the shape or rotating the figure while sliding.
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 Translations?
Slide a figure by a vector. It is a topic at the intermediate level in Geometry.
What is the formula for Translations?
The key formula is (x,y) → (x+a, y+b).
Where is Translations used in real life?
Real-world examples: Sliding tiles in a game; Moving a sprite across a screen; Shifting a pattern along a border.
What should I learn before Translations?
Make sure you are comfortable with Cavalieri’s Principle, the previous topic in Geometry.
What is a common mistake with Translations?
Changing the shape or rotating the figure while sliding.
How can I practise Translations?
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 Translations?
Move on to Reflections 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~.