Position and direction
Translation
A translation slides a shape to a new place. It does not turn it, flip it, or change its size — every point moves the same way.
What a translation is
A TRANSLATION slides a shape without turning or flipping it. Every point moves the same distance in the same direction, so the shape stays exactly the same size and the same way up. Only its position changes. The new shape is CONGRUENT to the old one — identical in shape and size.
Describing a translation
Give the movement across and the movement up or down: '4 squares to the right' '3 squares down' '1 square left and 2 squares up' Always say both parts if the shape moves diagonally. Saying only 'it moved' is not enough to describe it.
Translating a shape
Move every VERTEX by the same amount, then join them up. To translate a shape 3 right and 2 up, take each corner and move it 3 across and 2 up. Mark the new corners, then draw the sides. Moving the whole shape by eye usually distorts it — moving the corners one at a time does not.
What translation does NOT change
After a translation the shape has the same side lengths, the same angles, and the same area. It faces the same way. That is what makes it different from a REFLECTION, which flips the shape over, and a ROTATION, which turns it. If a shape has been turned or flipped, it has not been translated.
Worked examples
Describing a slide
- The shape has moved across to the right.
- Count the squares it moved: 4.
Answer: 4 squares to the right
A diagonal translation
- The shape moved 1 square to the left.
- It also moved 2 squares up.
- Both parts must be given.
Answer: 1 square left and 2 squares up
Translating a vertex
- A corner is at (2, 3).
- Translate 3 right and 2 up.
- 2 + 3 = 5 across, 3 + 2 = 5 up.
Answer: The corner moves to (5, 5)
Does the shape change size?
- Every point moves the same distance in the same direction.
- So the sides and angles are unchanged.
Answer: No — it stays exactly the same size
Translation or reflection?
- The shape is facing the opposite way.
- A translation never flips a shape.
Answer: It must be a reflection, not a translation
Where you see this in real life
- Moving a piece on a board game without turning it.
- Sliding a window or a drawer — it moves without rotating.
- Repeating patterns on wallpaper are made by translating one motif.
Key words
- Translation
- A slide that moves a shape without turning or flipping it.
- Vertex
- A corner of a shape.
- Congruent
- Identical in shape and size.
- Reflection
- A flip of a shape over a line.
- Rotation
- A turn of a shape about a point.
- Grid
- A pattern of squares used for plotting shapes.