Transformations change the position, size, or orientation of a shape. The four types tested at GCSE are translation, reflection, rotation, and enlargement.
The Four Transformations
Translation
Slides a shape by a vector .
- : horizontal movement (right +, left −)
- : vertical movement (up +, down −)
Shape and size stay the same.
Reflection
Flips a shape over a mirror line.
- Common lines: , -axis (), -axis (), .
- Each point is the same distance from the mirror line on the opposite side.
Rotation
Turns a shape around a centre point.
- Specify: angle, direction (clockwise/anticlockwise), and centre of rotation.
Enlargement
Changes the size using a scale factor from a centre of enlargement.
- Scale factor > 1: bigger.
- Scale factor between 0 and 1: smaller.
- Negative scale factor: inverted (other side of centre).
Describing Transformations
Always state the type and all required details:
- Translation: the vector.
- Reflection: the mirror line.
- Rotation: angle, direction, centre.
- Enlargement: scale factor, centre.
Practice Problems
- Translate triangle by .
- Reflect in the line .
- Rotate by clockwise about the origin.
- Enlarge by scale factor 2 from origin.
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Key Takeaways
Translation: vector. Reflection: mirror line. Rotation: angle + direction + centre. Enlargement: scale factor + centre.
Only enlargement changes the size.
Describe transformations with full details.
