Transformations

A transformation moves or changes a shape. Reflections flip it in a mirror line, rotations turn it about a point, translations slide it, and enlargements make it bigger or smaller by a scale factor.

Key facts

  • Reflection: every point ends up the same distance from the mirror line on the other side.
  • Rotation: give the angle, the direction and the centre.
  • Translation: a column vector, like 3 right and 2 down.
  • Enlargement: multiply distances from the centre by the scale factor.

Worked examples

Example 1

Reflect the triangle with corners (2, 1), (4, 1) and (4, 3) in the y-axis.

  1. Reflecting in the y-axis changes the sign of x and keeps y. (x, y) → (−x, y)
  2. So (−2, 1), (−4, 1), (−4, 3)

Answer: (−2, 1), (−4, 1), (−4, 3)

Example 2

Translate the point (−1, 2) by 3 right and 4 down. Where does it go?

  1. Right adds to x, down takes from y. (−1 + 3, 2 − 4)
  2. So (2, −2)

Answer: (2, −2)