1. Which transformation preserves size and orientation?
- Translation
- Enlargement by factor 2
- Reflection
Check the answer and reasoning
Translation
Translation moves every point by the same vector.
MATH / IGCSE
Transformations and vectors
Translations, reflections, rotations and enlargements map shapes while changing specified features. A vector describes displacement with magnitude and direction.
Learning objectives
- Explain transformations and vectors using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Translations, reflections, rotations and enlargements map shapes while changing specified features. A vector describes displacement with magnitude and direction.
Add vectors component by component or head to tail. A position vector depends on the chosen origin; the displacement from A to B is OB−OA.
Equations and relationships
Subtract starting position from finishing position.
Worked example
A = (1,2), B = (4,6). Find vector AB.
Follow the solution
Subtract components: (4−1,6−2) = (3,4).
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. A = (1,2), B = (4,6). Find vector AB.
- (5,8)
- (3,4)
- (−3,−4)
Check the answer and reasoning
(3,4)
Subtract components: (4−1,6−2) = (3,4).
3. What is the length of vector (3,4)?
- 7
- 25
- 5
Check the answer and reasoning
5
Pythagoras gives √(3²+4²) = 5; 25 is its squared length.