Transformations
Translations, rotations, reflections and enlargements (including negative scale factors at Higher).
Learn
Transformations, explained point by point
Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.
Reflect shapes in mirror lines, including lines like y = x
Each image point sits the same distance behind the mirror line as the original is in front, on a perpendicular path. For x = 2 or y = −1, count squares across or up; for y = x, coordinates swap - (3, 1) reflects to (1, 3). Tracing paper is allowed - use it.
Rotate shapes about a centre of rotation
A rotation needs an angle, a direction, and a centre - 90° clockwise about the origin, say. Tracing paper makes it mechanical: mark the centre, trace the shape, and turn. To FIND a centre, it is the one point that has not moved.
Translate shapes using column vectors
A translation slides every point by the same column vector - (−3 over 2) means 3 left, 2 up - with no turning or resizing. Move each vertex separately, then join them up.
Enlarge shapes from a centre, including fractional scale factors
Multiply each point's distance from the centre by the scale factor, along the line joining them. Scale factor 3 triples the distances; scale factor brings everything in to half - the shape SHRINKS, but it is still called an enlargement.
Enlarge shapes with negative scale factorsHigher only
A negative scale factor puts the image on the OPPOSITE side of the centre, upside down. With scale factor −2, each point lands twice as far away, straight through the centre. The image is inverted as well as resized.
Describe a transformation fully from a diagram
"Fully" means every ingredient: reflection - the mirror line's equation; rotation - angle, direction and centre; translation - the column vector; enlargement - scale factor and centre. And it is always ONE transformation; naming two scores zero.
Practice
Try a Transformations question
A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.
A translation maps A(−2, 3) to A′(1, 0). Which vector describes the translation?
- (−1, 3)
- (−3, 3)
- (3, 3)
- (3, −3)
Show the answer and the working
Answer: (3, −3)
Subtract the original coordinates from the image coordinates: 1 − (−2) = 3 and 0 − 3 = −3.
- The translation vector is image minus original, coordinate by coordinate.
- Horizontal part: 1 − (−2) = 1 + 2 = 3.
- Vertical part: 0 − 3 = −3.
- So the vector is (3, −3).