Translation: Sliding Shapes on a Grid

G18Translation

Slide it — same shape, new place.

Translation slides a shape left/right and up/down without turning or flipping it.

Translate the triangle 4 right, 2 up.

Every vertex moves the same way: +4 to x, +2 to y

Translation: add to x for right, add to y for up. The shape never turns.

Learn the 3-Step Method

1Read the instruction.

‘4 right, 2 up’ means x + 4 and y + 2.

x+4, y+2

2Move every vertex.

Apply the same shift to each corner: (1, 1) → (5, 3).

(1,1) → (5,3)

3Check the shape.

Same size, same way up, new position. Label the image A′, B′, C′.

identical, moved

💡 Key IdeaLeft and down mean subtracting: 3 left, 1 down turns (5, 4) into (2, 3).

Worked Example

Translate the point (2, 5) by 3 right and 4 down.

x: 3 right

2 + 3 = 5

→

y: 4 down

5 − 4 = 1

→

✓ Answer

(5, 1)

Watch Out! Common Mistakes

Moving only one vertex.

Move them all! Every vertex shifts by the same amount — shift one and redraw, and the shape distorts.

Mixing up the directions.

4 down: y = 5 + 4 = 9 ✕

Wrong sign! Down means subtract from y: 5 − 4 = 1.

Turning the shape as it moves.

Never! Translation only slides. If the shape has rotated or flipped, it isn’t a translation.

⬇ Cheat Sheet

TRANSLATION

Right: add to x. Left: subtract from x.
Up: add to y. Down: subtract from y.
Move every vertex by the same amounts.
The shape stays identical — just relocated.

Example: (2, 5) → 3 right, 4 down → (5, 1).

📄 Free printable: Download the Translation cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Translation slides a shape; it never rotates or reflects.
Right/up add to x/y; left/down subtract.
Apply the same shift to every vertex.
(2, 5) translated 3 right and 4 down becomes (5, 1).

Frequently asked questions

What is a translation in maths?

A transformation that slides a shape to a new position without rotating, reflecting or resizing it — every point moves the same distance in the same direction.

How do you translate a coordinate?

Add or subtract from each part: 3 right and 4 down turns (2, 5) into (2+3, 5−4) = (5, 1).

How can children check a translation?

The image should be identical to the original — same size, same way up — and every vertex should have moved by exactly the same amounts.

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G17 Coordinates (Four Quadrants)

Translation