Sheet № 172 · Foundation + Higher · AQA · Edexcel · OCR
Describing Transformations –
"Fully describe the single transformation" is one of the most common GCSE instructions — and one of the easiest to lose marks on. Each transformation requires specific pieces of information, and missing any one of them means lost marks.
§Key definitions
Question:
Shape A is mapped to Shape B by a reflection. Shape A has vertices at (1, 2), (1, 5), (3, 5). Shape B has vertices at (5, 2), (5, 5), (3, 5). Fully describe the transformation.
Answer:
Reflection in the line x = 3.
Q1 (Foundation):
Shape A is translated so that point (2, 3) moves to (5, 1). Write down the column vector of the translation.
Q2 (Foundation):
Shape P is reflected in the y-axis. Describe what happens to the point (4, 7).
Q3 (Higher):
Triangle A is mapped to Triangle B by a rotation of 180° about the point (1, 2). Point (3, 5) is a vertex of A. Find the corresponding vertex of B.
§Formulas to memorise
Translation is described using a column vector: (x y) where x is horizontal movement and y is vertical movement
Enlargement scale factor = new length ÷ original length
Reflection: — the equation of the mirror line (e.g., x = 2 or y = x).
Rotation: — the angle, the direction (clockwise or anticlockwise), and the centre of rotation.
Translation: — the column vector.
Enlargement: — the scale factor and the centre of enlargement.
What you need for each transformation:: - Reflection: the equation of the mirror line (e.g., x = 2 or y = x).
Worked example
Shape A is mapped to Shape B by a reflection. Shape A has vertices at (1, 2), (1, 5), (3, 5). Shape B has vertices at (5, 2), (5, 5), (3, 5). Fully describe the transformation.
Working: The shapes are mirror images. The midpoint of (1, 2) and (5, 2) is (3, 2). The midpoint of (1, 5) and (5, 5) is (3, 5). The mirror line passes through x = 3.
⚠ Common mistakes
- ✗Not naming the transformation. You must state "reflection," "rotation," "translation," or "enlargement" — this is usually worth one mark on its own.
- ✗Missing the mirror line equation for reflections. Writing "reflected" without the line equation (e.g., y = −1 or x = 3) is incomplete.
- ✗Forgetting the direction for rotations. You must state clockwise or anticlockwise (unless the angle is 180°, where direction is irrelevant).
- ✗Giving coordinates instead of a column vector for translations. A translation must be described with a column vector, not as a set of coordinates.
- ✗Not finding the centre for enlargements. The centre of enlargement is essential — draw ray lines through corresponding vertices to locate it.
✦ Exam tips
- →Count the details needed: reflection needs 2 (name + line), rotation needs 4 (name + angle + direction + centre), translation needs 2 (name + vector), enlargement needs 3 (name + scale factor + centre).
- →A negative scale factor (Higher) means the image is on the opposite side of the centre and inverted.
- →Fractional scale factors (e.g., ½) produce a smaller image — still called an "enlargement."
- →For combined transformations, apply each transformation in order, then describe the net effect as a single transformation.