GEOMETRY

Coordinates

Learn the reliable method for coordinates, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Coordinates describe a point by horizontal position first and vertical position second.

Picture itMove across first, then up
2 · THE METHOD

Follow these steps

  1. Read or change the x-coordinate first.
  2. Read or change the y-coordinate second.
  3. For transformations, apply the stated movement to every vertex.
3 · WORKED EXAMPLES

See the method in action

Example 1

Point P is moved 3 squares right and 2 squares up to P′(6, 5). What were the coordinates of P?

024682468xyP′
  1. Work backwards: subtract 3 from the x-coordinate and 2 from the y-coordinate to get (3, 3).
Answer: (3, 3)
Example 2

Use the labelled coordinate diagram. Point P is reflected in the y-axis, then translated by the shown vector. What are its final coordinates?

-4-224-4-224xyP(-5, 5)translation vector = (4, -3)
  1. Reflection in the y-axis changes P to (5, 5).
  2. Adding the translation vector (4, -3) gives (9, 2).
Answer: (9, 2)
4 · ELEVENSPRINT TIP

A useful shortcut

For transformations, apply the stated movement to every vertex.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.