Transformations · Grade 10

In Grade 10 you learn: negative and fractional scale factors.

A transformation moves a shape. Reflections, rotations and translations keep the size and shape the same (the image is congruent); an enlargement changes the size by a scale factor but keeps the shape (the image is similar).

Key facts

  • Reflection: in a mirror line; in the x-axis (x, y) → (x, −y); in the y-axis (x, y) → (−x, y).
  • Rotation: give the angle, direction and centre. 180° about the origin: (x, y) → (−x, −y).
  • Translation: a column vector (a, b) means a right and b up.
  • Enlargement: give the scale factor and centre; every length is multiplied by the scale factor.
  • Areas scale by the scale factor squared.

Worked examples

Example 1

Describe the single transformation that maps triangle A onto triangle B.

Answer: A reflection in the y-axis (the line x = 0)

Example 2

Rotate P(4, 1) through 90° anticlockwise about the origin. Where does it land?

Answer: (−1, 4)

Example 3

Enlarge P(3, 2) by scale factor 2 with centre (1, 1).

Answer: (5, 3)

Other years