Translation and reflection
- A translation slides a shape without turning it. Describe it by how far it moves right or left and up or down (a vector): 3 right and 2 down.
- A reflection flips a shape in a mirror line, such as the x-axis, the y-axis, x = 2 or y = x. Each point ends up the same distance from the line, on the other side.
- Reflecting (2, 5) in the x-axis gives (2, −5); reflecting it in the y-axis gives (−2, 5).
Rotation
- A rotation turns a shape about a centre of rotation. Describe the angle, the direction (clockwise or anticlockwise) and the centre.
- A rotation of 180° about the origin changes (4, 2) into (−4, −2).
- Use tracing paper to help you rotate shapes.
Enlargement
- An enlargement changes the size of a shape by a scale factor, from a centre of enlargement. A scale factor of 2 doubles every length; a scale factor of ½ halves them.
- The angles stay the same, so the image is similar to the original. If the scale factor is 2, the area is multiplied by 4.
- Translations, reflections and rotations give congruent images (the same size); enlargements give similar images.
Key terms
- Transformation
- A change to the position, direction or size of a shape.
- Translation
- Sliding a shape without turning or resizing it.
- Reflection
- Flipping a shape in a mirror line.
- Rotation
- Turning a shape about a fixed point.
- Enlargement
- Changing the size of a shape by a scale factor.
- Scale factor
- The number that all the lengths are multiplied by in an enlargement.
- Centre of rotation
- The fixed point a shape turns around.
- Mirror line
- The line a shape is reflected in.
- Image
- The shape after a transformation.
- Vector
- A way of describing a movement: how far across and how far up or down.