Translation
Slides every point by the same vector.
🎯 Learning Objectives
- define a transformation, object and image;
- identify translations, reflections, rotations and enlargements;
- understand congruence, similarity and orientation;
- describe a transformation using complete information.
Introduction
This lesson develops Introduction to Transformations from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
What Is a Transformation?
A transformation maps every point of a shape to a new position. The starting shape is the object and the resulting shape is the image .
A complete description tells another student exactly how to reproduce the image.
Four Main Transformations
Reflection
Flips a figure across a mirror line.
Rotation
Turns a figure around a fixed centre.
Enlargement
Changes size from a centre using a scale factor.
What Can Change?
Position, orientation and size may change. Shape is preserved in translations, reflections, rotations and enlargements.
Practice Questions
- Define object and image.
- Which transformations preserve size?
- Which transformation needs a mirror line?
- What information is needed to describe a rotation completely?
✅ Check Your Work
Show answers and working
- Object: original figure. Image: resulting figure after the mapping.
- Translation, reflection and rotation preserve size.
- Reflection.
- Centre of rotation, angle and direction.
🧠 Learn It Visually: What Is a Transformation?
A transformation is a rule that maps every point of an object to a new point in an image. We use a prime mark, such as A′, to name the image of A.
Object and image
The original figure is the object. The figure after the rule is applied is the image.
Mapping
A → A′ means point A maps to point A-prime.
What can change?
Position, orientation, size or shape may change. Some features may remain invariant.
🎯 Identify the Transformation
Study the object and image, then choose the most complete description.
Look at size, orientation and corresponding movements.
Think Like a Mathematician: If two figures have the same shape and size but different positions, which transformations could have produced the image?
🧷 Remember
Describe a transformation by comparing corresponding points—not by judging the picture casually.
⚠️ Common Mistake
Do not call every movement a translation. A reflection changes orientation; a rotation turns around a centre.
🎯 Exam Tip
A complete description often needs extra information: vector, mirror line, centre and angle, or centre and scale factor.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.