Triangle A has vertices (1, 2), (4, 2) and (1, 6). Triangle A is rotated 90^ anticlockwise about the origin. Write down the coordinates of the images of the vertices (4, 2) and (1, 6).

image of (4, 2): x = -2, image of (4, 2): y = 4, image of (1, 6): x = -6, image of (1, 6): y = 1

A designer draws a logo on a coordinate grid where 1 unit represents 1 cm. The logo is a triangle with vertices (2, 1), (5, 1) and (2, 3). For a poster the logo is enlarged by scale factor 4, centre the origin. Write down the coordinates of the image of (5, 1), and the length in cm of the image of the side joining (2, 1) to (5, 1).

image x = 20, image y = 4, length in cm = 12

A shape is reflected in the x-axis and then reflected in the y-axis. Which single transformation has the same effect?

Rotation of 180^ about the origin

Rotation of 90^ clockwise about the origin

Triangle P has vertices (1, 2), (7, 2) and (1, 6). Triangle Q has vertices (4, 4), (7, 4) and (4, 6). Q is the image of P under an enlargement. Find the scale factor and the coordinates of the centre of enlargement.

scale factor = 0.5, centre x = 7, centre y = 6

A shape is reflected in the x-axis and then rotated 90^ anticlockwise about the origin. Which single transformation has the same effect?

Rotation of 90^ anticlockwise about the origin

Rotation of 180^ about the origin

Are negative scale factors on the Foundation paper?

No. G7 reads the same at both tiers except for one phrase: Foundation covers enlargement including fractional scale factors, and Higher covers fractional and negative scale factors. So a fractional enlargement such as scale factor one half can appear at either tier, while an enlargement of scale factor minus two is Higher only. The same is true of G8, describing the changes and invariance achieved by combinations of rotations, reflections and translations, which is Higher content in full.

How do you describe a transformation fully in the exam?

Name the transformation, then give the details that type needs. A translation needs a column vector. A reflection needs the equation of the mirror line, written as an equation such as y = x or x = 3 rather than a description of where it sits. A rotation needs the angle, the direction and the coordinates of the centre. An enlargement needs the scale factor and the coordinates of the centre. If the question says single transformation, give exactly one.

How many marks are transformation questions worth on Edexcel Higher?

A single drawing instruction or a single description is usually 2-3 marks, and a paper often carries one of each, so expect roughly 3-6 marks per paper. The heavier versions are the ones that combine two transformations and then ask for the equivalent single transformation, or that ask you to find the centre of an enlargement rather than use one you are given.

Is anything about transformations on the Edexcel formulae sheet?

No. The Exam Aid formulae sheet issued with 1MA1 papers carries the trapezium, prism and circle formulae, the quadratic formula, Pythagoras, the trigonometric ratios and rules, compound interest and two probability rules. Nothing from G7 or G8 is on it, so the rules for reflecting in y = x, rotating about a point and enlarging from a centre are all recall. Tracing paper is allowed, which is the one piece of help the exam does give you.

Transformations - Edexcel GCSE Higher Maths

Typically 3-6 marks per paper, usually one shape to draw and one to describe fully · Spec 1MA1

A transformation moves a shape, turns it, flips it or resizes it. Edexcel splits the work over two references on the 1MA1 specification. G7 asks you to identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement, and the Higher version of that line adds negative scale factors to the fractional ones both tiers meet. G8 is Higher only: describe the changes and invariance achieved by combinations of rotations, reflections and translations. Translations are written as column vectors, which is where the topic runs into G24. Three of the four transformations leave the image congruent to the object; enlargement is the one that changes size, and it is the reason this topic feeds straight into similar shapes.

On a real paper the shapes sit on a squared grid and the question usually comes in two parts. One part gives an instruction to carry out, rotate the shape $90^\circ$ clockwise about $(0, 1)$ , or enlarge it by scale factor $-2$ with centre $(0, 2)$ , and wants the image drawn and labelled. The other shows two shapes already drawn and says 'describe fully the single transformation that maps shape A onto shape B'. Each part is normally 2-3 marks. Transformations turn up on Paper 1, 2 or 3 and a calculator changes nothing about them, so the non-calculator paper is as likely as either of the others. Tracing paper is allowed in the exam, and it is the quickest way to settle a rotation or to test whether a point really is the centre.

The describing half is where the marks go missing. 'Describe fully' is close to all or nothing: a rotation needs the angle, the direction and the centre; an enlargement needs the scale factor and the centre; a reflection needs the equation of the mirror line, so 'reflected in the diagonal' earns nothing where $y = x$ would have earned everything; a translation needs a column vector rather than a sentence about moving across and up. Name two transformations when the question said one and the marks go even if both are right. The second regular loss is direction. A question mapping A onto B is not the same as one mapping B onto A, and the vector, the scale factor and the sense of the rotation all reverse when the mapping is read the wrong way round.

Worked example

Triangle A has vertices

(3, 2)

(7, 2)

and

(3, 4)

. Triangle B has vertices

(5, 5)

(13, 5)

and

(5, 9)

. B is the image of A under a single enlargement. Describe the enlargement fully.

[4 marks]

Compare a pair of corresponding sides. The side from $(3, 2)$ to $(7, 2)$ is 4 units long; its image from $(5, 5)$ to $(13, 5)$ is 8 units long. The scale factor is $\frac{8}{4} = 2$ .
M1: scale factor from one pair of corresponding sides, image length divided by object length
Let the centre be $(a, b)$ . Each vertex ends up twice as far from the centre along the same line, so the image $x$ -coordinate is $a + 2(x - a)$ . For $(3, 2)$ going to $(5, 5)$ that gives $a + 2(3 - a) = 5$ , so $6 - a = 5$ and $a = 1$ .
M1: a correct equation in one coordinate of the centre; distances are measured from the centre, not from the origin
Do the same with the $y$ -coordinates: $b + 2(2 - b) = 5$ , so $4 - b = 5$ and $b = -1$ . The centre is $(1, -1)$ .
A1: centre $(1, -1)$ ; a negative coordinate here is exactly what catches candidates who guessed from the picture
Check on a second vertex: from $(1, -1)$ to $(3, 4)$ is 2 across and 5 up, doubled is 4 across and 10 up, landing on $(5, 9)$ , which is a vertex of B. Write the answer as one sentence: enlargement, scale factor 2, centre $(1, -1)$ .
A1: all three elements stated together; naming the transformation without the centre would lose this mark

Practice questions

These are original questions in Edexcel 1MA1 Higher style. There are no diagrams, so every shape is given by its vertex coordinates and every answer is a set of coordinates, a scale factor or a description chosen from four options. Working without a grid is stricter than the exam version, so lean on the rules: a translation adds the column vector, a reflection in $y = x$ swaps the coordinates, and an enlargement counts from its centre rather than from the origin. None of it needs a calculator, so it doubles as Paper 1 practice.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [2 marks]

Triangle $A$ has vertices $(1, 2)$ , $(4, 2)$ and $(1, 6)$ . Triangle $A$ is enlarged by scale factor 3, centre the origin. Write down the coordinates of the image of the vertex $(4, 2)$ .

x = y =
Question 2 Exam pace [3 marks]

Triangle $A$ has vertices $(1, 2)$ , $(4, 2)$ and $(1, 6)$ . Triangle $A$ is rotated $90^\circ$ anticlockwise about the origin. Write down the coordinates of the images of the vertices $(4, 2)$ and $(1, 6)$ .

image of (4, 2): x = image of (4, 2): y = image of (1, 6): x = image of (1, 6): y =
Question 3 Exam pace [3 marks]

A designer draws a logo on a coordinate grid where 1 unit represents 1 cm. The logo is a triangle with vertices $(2, 1)$ , $(5, 1)$ and $(2, 3)$ . For a poster the logo is enlarged by scale factor 4, centre the origin. Write down the coordinates of the image of $(5, 1)$ , and the length in cm of the image of the side joining $(2, 1)$ to $(5, 1)$ .

image x = image y = length in cm =
Question 4 Exam pace [1 mark]

A shape is reflected in the $x$ -axis and then reflected in the $y$ -axis. Which single transformation has the same effect?

Answer options for question 4
Rotation of $180^\circ$ about the origin Reflection in the line $y = x$ Reflection in the line $y = -x$ Rotation of $90^\circ$ clockwise about the origin
Question 5 Stretch [4 marks]

Triangle $P$ has vertices $(1, 2)$ , $(7, 2)$ and $(1, 6)$ . Triangle $Q$ has vertices $(4, 4)$ , $(7, 4)$ and $(4, 6)$ . $Q$ is the image of $P$ under an enlargement. Find the scale factor and the coordinates of the centre of enlargement.

scale factor = centre x = centre y =
Question 6 Stretch [1 mark]

A shape is reflected in the $x$ -axis and then rotated $90^\circ$ anticlockwise about the origin. Which single transformation has the same effect?

Answer options for question 6
Reflection in the line $y = x$ Reflection in the line $y = -x$ Rotation of $90^\circ$ anticlockwise about the origin Rotation of $180^\circ$ about the origin

Common mistakes examiners see

Answering 'describe fully the single transformation' with two transformations, for example 'reflection in the $y$ -axis, then a translation of 4 up'. Both halves can be correct and the answer still scores zero.

Read the word 'single' as an instruction, then find the one move that does the whole job. Two reflections in parallel mirrors combine into a translation; two reflections in perpendicular mirrors combine into a rotation of $180^\circ$ about the point where they cross. If the object and the image are different sizes, the single transformation has to be an enlargement.
Giving an incomplete description: 'enlargement, scale factor 3' with no centre, or 'rotation of $90^\circ$ about $(0, 0)$ ' with no direction. Partial descriptions are the most common way these marks are lost.

Learn the four checklists and write them down before you answer. Translation: column vector. Reflection: the equation of the mirror line. Rotation: angle, direction, centre. Enlargement: scale factor, centre. Count the items in your sentence against the list before moving on.
Mishandling a negative scale factor. Enlarging by $-2$ and either making the shape half the size, or doubling it on the same side of the centre as the object.

Treat the sign and the size separately. The size comes from the 2, so every length doubles; the minus sign sends the image through the centre to the opposite side, which turns it upside down. Count from the centre to a vertex, then count double that distance in the opposite direction.
Multiplying the coordinates by the scale factor when the centre is not the origin. With scale factor 3 and centre $(2, 1)$ , the vertex $(4, 3)$ is given as $(12, 9)$ instead of $(8, 7)$ .

Work with the step from the centre, not with the coordinates. From $(2, 1)$ to $(4, 3)$ is 2 across and 2 up; tripled that is 6 across and 6 up; starting again at $(2, 1)$ that lands on $(8, 7)$ . Multiplying coordinates only works when the centre happens to be $(0, 0)$ .
Confusing $y = x$ with $y = -x$ , so $(5, -2)$ reflects to $(2, -5)$ when the answer should be $(-2, 5)$ , or naming the mirror as 'the diagonal' with no equation at all.

For $y = x$ swap the two coordinates and stop. For $y = -x$ swap them and change both signs. Then sanity check one vertex by eye: the mirror line must sit halfway between the point and its image, at right angles to the line joining them.

Frequently asked questions

Are negative scale factors on the Foundation paper?: No. G7 reads the same at both tiers except for one phrase: Foundation covers enlargement including fractional scale factors, and Higher covers fractional and negative scale factors. So a fractional enlargement such as scale factor one half can appear at either tier, while an enlargement of scale factor minus two is Higher only. The same is true of G8, describing the changes and invariance achieved by combinations of rotations, reflections and translations, which is Higher content in full.
How do you describe a transformation fully in the exam?: Name the transformation, then give the details that type needs. A translation needs a column vector. A reflection needs the equation of the mirror line, written as an equation such as y = x or x = 3 rather than a description of where it sits. A rotation needs the angle, the direction and the coordinates of the centre. An enlargement needs the scale factor and the coordinates of the centre. If the question says single transformation, give exactly one.
How many marks are transformation questions worth on Edexcel Higher?: A single drawing instruction or a single description is usually 2-3 marks, and a paper often carries one of each, so expect roughly 3-6 marks per paper. The heavier versions are the ones that combine two transformations and then ask for the equivalent single transformation, or that ask you to find the centre of an enlargement rather than use one you are given.
Is anything about transformations on the Edexcel formulae sheet?: No. The Exam Aid formulae sheet issued with 1MA1 papers carries the trapezium, prism and circle formulae, the quadratic formula, Pythagoras, the trigonometric ratios and rules, compound interest and two probability rules. Nothing from G7 or G8 is on it, so the rules for reflecting in y = x, rotating about a point and enlarging from a centre are all recall. Tracing paper is allowed, which is the one piece of help the exam does give you.

Transformations - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics