Translate, reflect & rotate shapes
Theory
A translation slides a shape, a reflection flips it over a mirror line, and a rotation turns it about a point. All three move the shape without changing its size, so the image is congruent to the original.
A transformation moves a shape to a new position. Three transformations keep the shape exactly the same size and shape.
A translation slides the shape: every point moves the same distance in the same direction.
A reflection flips the shape over a mirror line, so the image faces the opposite way.
A rotation turns the shape about a fixed point. After any of these moves the image is congruent to the original.
Each move changes position only. What stays the same and what changes is set out below.
| Move | What it does | Size and shape |
|---|---|---|
| Translation | slides | unchanged |
| Reflection | flips over a line | unchanged |
| Rotation | turns about a point | unchanged |
How to name a transformation
- Compare the way each shape faces. Same way up and same direction points to a slide.
- Check for a flip. If the image is a mirror image, it is a reflection.
- Check for a turn. If the image is turned about a point, it is a rotation.
Every point slides the same way, so it is a translation.
The shape is flipped over the line, so it is a reflection.
A rotation keeps size and shape, so the image is congruent to the triangle.
| \((2+4,\ 3-1)\) | \(=\) | \((6,2)\) |
Common pitfalls
Frequently asked questions
What is a translation?
A translation slides a shape so that every point moves the same distance in the same direction. The shape keeps the same size, shape and way up.
What is the difference between a reflection and a rotation?
A reflection flips a shape over a mirror line, giving a mirror image. A rotation turns a shape about a point, so it faces a new direction without being flipped.
Do these transformations change the size of a shape?
No. Translations, reflections and rotations all keep the size and shape the same. The image is congruent to the original.
What does congruent mean?
Congruent shapes are exactly the same size and shape. They can be placed on top of each other so they match perfectly.
How can I tell which transformation was used?
Compare a shape with its image. If it has slid, it is a translation; if it is a mirror image, a reflection; if it has turned about a point, a rotation.