GEOMETRY

Reflections

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

1 · WHAT YOU NEED TO KNOW

The idea

Reflections questions require you to use properties and labels, not the apparent size of a drawing.

Picture itMatch both sides across the mirror line
2 · THE METHOD

Follow these steps

  1. Mark the information given on the diagram.
  2. Choose the relevant property or formula.
  3. Calculate one step at a time and include units.
3 · WORKED EXAMPLES

See the method in action

Example 1

Point P(5, 4) is reflected in the y-axis. What are the coordinates of its image?

P(5, 4)
  1. A reflection in the y-axis keeps y and changes x, giving (-5, 4).
Answer: (-5, 4)
Example 2

Vertex C(-2, 4) is reflected in the origin, then translated by (3, -1). What are its final coordinates?

Reflect in the origin, then translate by (3, -1)-4-224-4-224xyABC
  1. Reflection in the origin changes both signs to (2, -4).
  2. Translation gives (5, -5).
Answer: (5, -5)
4 · ELEVENSPRINT TIP

A useful shortcut

Never rely on a diagram being drawn to scale unless the question says it is.

5 · COMMON MISTAKES

Watch out for these

Using a remembered number without checking the shape

Name the shape or angle rule before substituting values.

6 · TRY IT YOURSELF

Three fresh questions

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