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Coordinates and translations

Coordinates give a point's position as (across, up). Grids can have four quadrants, so negative numbers appear. A translation slides a shape without turning it; a reflection flips it in a mirror line.

What is tested

  • Reading and plotting points in all four quadrants
  • Translating a point or shape (so many right/left and up/down)
  • Reflecting in the x-axis or y-axis, and finding missing corners of shapes

Worked example

Point A is at (−3, 2). It is translated 5 squares right and 4 squares down. Where does it end up?

  1. Right and left change the first number: −3 + 5 = 2.
  2. Up and down change the second number: 2 − 4 = −2.
  3. Write it as (across, up).

Answer: (2, −2)

Exam-day checklist

  • Along the corridor, then up the stairs: (x, y).
  • Right is +, left is −, up is +, down is −.
  • Reflecting in the x-axis changes the sign of y; in the y-axis, the sign of x.
  • Sketch a quick grid to check.

Common mistakes

  • Writing the coordinates the wrong way round.
  • Counting the starting square when moving.
  • Changing the wrong number in a reflection.

Try it yourself

1. Point (3, 5) is reflected in the x-axis. Where is its image?

Show answer

(3, −5)

Reflecting in the x-axis keeps x the same and changes the sign of y.

2. A square has corners at (1, 1), (4, 1) and (4, 4). Where is the fourth corner?

Show answer

(1, 4)

The sides are 3 long, so the missing corner is 3 above (1, 1).

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