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Translating 2D shapes

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Position and transformation

Translating 2D shapes

Translating a shape slides it ā€” no turning, no flipping, no resizing. Every point moves the same distance in the same direction, so you can work out the new coordinates without drawing anything.

3 right, 1 up

Object and image

The shape you start with is the OBJECT. The shape after the move is the IMAGE. If triangle ABC is translated, its image is triangle A'B'C' ā€” said 'A dash, B dash, C dash'. Point A' CORRESPONDS to point A. They are the same corner, before and after.

What the move does to the coordinates

Translate triangle ABC 3 squares right and 2 squares up, and every vertex moves the same way: ā€¢ 3 right ā†’ add 3 to every x-coordinate ā€¢ 2 up ā†’ add 2 to every y-coordinate A(1, 1) ā†’ A'(4, 3) B(2, 3) ā†’ B'(5, 5) C(4, 1) ā†’ C'(7, 3) No grid needed.

Left and down are subtractions

Right and up ADD. Left and down SUBTRACT. Translate ABCD 2 squares right and 1 square down: add 2 to each x, subtract 1 from each y. A(2, 1) ā†’ A'(4, 0) B(5, 2) ā†’ B'(7, 1) C(4, 5) ā†’ C'(6, 4) D(1, 4) ā†’ D'(3, 3)

What stays the same

A translation only slides. It does not turn the shape, flip it or change its size. So the object and the image are CONGRUENT ā€” identical in shape and size, just somewhere else. Every side is the same length as before and every angle is the same size.

Worked examples

A(1, 1) translated 3 right and 2 up

  1. 3 right means add 3 to the x-coordinate.
  2. 2 up means add 2 to the y-coordinate.
  3. 1 + 3 = 4 and 1 + 2 = 3.

Answer: A'(4, 3)

B(2, 3) under the same translation

  1. 2 + 3 = 5 and 3 + 2 = 5.

Answer: B'(5, 5)

A(2, 1) translated 2 right and 1 down

  1. 2 right: add 2 to x, giving 4.
  2. 1 down: subtract 1 from y, giving 0.

Answer: A'(4, 0)

C(4, 5) under the same translation

  1. 4 + 2 = 6.
  2. 5 āˆ’ 1 = 4.

Answer: C'(6, 4)

A point translated 4 left and 3 down

  1. Left means subtract from x.
  2. Down means subtract from y.
  3. So (7, 8) becomes (7 āˆ’ 4, 8 āˆ’ 3).

Answer: (3, 5)

Is the image the same size?

  1. A translation only slides the shape.
  2. Nothing is turned, flipped or resized.

Answer: Yes ā€” the object and image are congruent

Where you see this in real life

  • Dragging an icon across a screen is a translation. Its shape and size never change, only its position.
  • A conveyor belt translates everything on it by the same amount, which is why the spacing between items stays fixed.

Key words

Translate
slide a shape without turning or flipping it
Object
the shape you start with
Image
the shape after the transformation
Corresponds
matches ā€” A' corresponds to A
Congruent
exactly the same shape and size
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