Each transformation needs its own details
Translation → a column vector. Reflection → the equation of the mirror line. Rotation → angle, direction and centre. Enlargement → scale factor and centre. Give ALL parts.
Negative and fractional scale factors
A scale factor between −1 and 1 makes the image smaller; a negative scale factor also turns the image through the centre to the opposite side (and inverts it).
Drawn from real examiner reports.
Giving two when a single is asked
When the question says "single transformation", naming a second transformation (or "enlargement and translation") loses the mark even if one part is right.
Reported on Nov 2023 Paper 2H (Q3b): "Students often said Enlargement to gain B1 but if they also gave another transformation this mark was withheld as a single transformation was requested." The paper summary lists: "Learn how to describe transformations using a single transformation."
Omitting the centre of an enlargement
Stating the scale factor but not the centre of enlargement only earns part of the marks.
Reported on Nov 2023 Paper 2H (Q3b): "Scale factor 3 often gained a mark, but the mark for finding the centre of enlargement was only scored by the more able students."
Struggling to reflect in a diagonal line
Reflecting in a line such as or is done less accurately than reflecting in a horizontal or vertical line.
Reported on Nov 2023 Paper 2H (Q3a): "Reflecting in a diagonal line in (a) was difficult for some number of students."
Enlarging from O, not the given centre
When the centre is not the origin, use image = centre + k(point − centre). Simply multiplying the coordinates by k enlarges from the origin, giving the wrong image whenever the centre is elsewhere.
Rotating the wrong way round
A rotation needs a direction: clockwise and anticlockwise give different images. For a 90° turn about O, anticlockwise sends but clockwise sends .
Reflecting in y = x: swap the coordinates
Under a reflection in , the point . Under , . Checking one vertex with this rule catches diagonal-mirror errors.
Single transformation means exactly one
When the question says "single transformation", give one only. Adding a second (e.g. "enlargement and translation") withholds the mark even if the first part is right. Describe it fully with all its parts.
Find the centre by joining points
To locate a centre of enlargement, draw straight lines through pairs of corresponding points (object vertex to image vertex). The lines meet at the centre — then state the scale factor and this centre.
| Transformation | You must state |
|---|---|
| Translation | a column vector |
| Reflection | the equation of the mirror line (e.g. , ) |
| Rotation | angle, direction (clockwise/anticlockwise) and centre |
| Enlargement | scale factor and centre |
If a question asks for a single transformation, give exactly one — naming a second one withholds the mark.
A question asks for a single transformation — why lose a mark by naming two?
The point has coordinates . is translated by the vector . Find the coordinates of the image .
