A rigid transformation moves a shape without changing its size or shape. Lengths and angles survive untouched.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Translation
A translation slides every point the same distance in the same direction. Adding 3 to every x-coordinate slides the shape right by 3.
Reflection
A reflection flips the shape across a line. Reflecting across the x-axis negates every y-coordinate.
Rotation
A rotation turns the shape about a fixed centre by a given angle. A 180° turn about the origin negates both coordinates.
Reflection is the odd one out
Translations and rotations preserve orientation. A reflection reverses it, which is why a reflected hand becomes the other hand.
Combining them
Applying several rigid transformations in turn is still rigid. The result is always congruent to the original.
Three moves that change nothing but position
Translation, reflection and rotation preserve every length and every angle. They are called rigid because the figure behaves like a solid object being moved.
Reflections reverse orientation
A reflected figure faces the other way and cannot be slid onto the original within the plane. That distinction matters for letters, hands and chemistry, and is the one property reflections do not preserve.
Each has a coordinate rule
Translation adds constants; reflection in an axis negates one coordinate; a quarter turn about the origin sends (x, y) to (−y, x). Algebraic rules let transformations be computed rather than drawn.
A description must be complete
A translation needs direction and distance; a reflection needs the mirror line; a rotation needs centre, angle and direction. Naming the move without those details does not determine the result.
Step 2: Try It Yourself
Tap and try it out.
Every length and every angle is exactly as it was. The shape moved without changing, so the two figures are congruent.
Step 3: Watch an Example
One step at a time.
Watch Kofi Reflect a Point
Kofi reflects the point (4, 3) across the x-axis.
- Step 1
A reflection across the x-axis leaves horizontal position alone, so x stays 4.
Step 4: Your Turn
Practice makes it stick.
The Slide
Problem 1 of 2
Translate (2, 5) right by 4. What is the new x-coordinate?
The Flip
Problem 2 of 2
Reflect (4, 3) across the x-axis. What is the new y-coordinate?
Move the Shape
1 of 8
Translate (1, 1) up by 5. New y-coordinate?
2 of 8
Reflect (7, 2) across the y-axis. New x-coordinate?
3 of 8
Rotate (3, 5) by 180° about the origin. New x-coordinate?
4 of 8
Same rotation. New y-coordinate?
5 of 8
A shape has side 8. After a translation, what is that side length?
6 of 8
Which transformation reverses orientation? 1 translation, 2 reflection.
7 of 8
Match each transformation with its effect on a point.
Tap a card on the left to start.
8 of 8
Translate (5, 5) left by 8. New x-coordinate?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Reflect (6, 2) across the y-axis. New x-coordinate?
Question 2 of 2
What does a rigid transformation preserve?
What You Learned
- Rigid transformations preserve lengths and angles.
- Translations slide, reflections flip, and rotations turn.
- Only reflections reverse orientation.