A transformation moves or changes a shape. You must be able to perform each type and describe it fully. The original shape is the object; the result is the image.
The four transformations
- Translation — a slide, described by a column vector giving movement right/left and up/down.
- Reflection — a flip in a mirror line (such as the x-axis, y-axis or y = x).
- Rotation — a turn, described by a centre, an angle and a direction.
- Enlargement — a resize, described by a centre and a scale factor k.
Key idea
Under an enlargement of scale factor k, every length is multiplied by k and the area is multiplied by k2. Reflection, rotation and translation keep the shape and size unchanged (congruent), so the object and image are identical apart from position. Only enlargement changes the size, giving an image that is similar to the object.
When you are asked to describe a single transformation fully, name the type first and then give every detail it needs: the vector for a translation, the mirror line for a reflection, the centre, angle and direction for a rotation, and the centre and scale factor for an enlargement. Missing any of these loses marks even if the type is correct.
Worked example
Worked example
A triangle has area 5 cm2. It is enlarged by scale factor 3 about the origin. Find the area of the image.
Area of image = 5 × 32 = 5 × 9 = 45 cm2.
Also, the point (3, 4) maps to (3×3, 4×3) = (9, 12).
Remember
- To describe a rotation you need centre, angle and direction.
- To describe an enlargement you need centre and scale factor.
- Rotation 180° about the origin sends (x, y) to (−x, −y).