What is G7: Transformations?

Describe a transformation completely: a translation needs a column vector; a rotation needs centre, angle and direction; a reflection needs its mirror line; an enlargement needs centre and scale factor. Translation, rotation and reflection preserve every length and angle, so object and image are congruent.

How many marks are G7 questions worth?

In verified past-paper appearances, G7 questions on Edexcel GCSE Maths 1MA1 have been worth 1–4 marks.

Which past exam papers has G7 appeared in?

G7 has appeared in 26 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Identify, describe and construct congruent and similar shapes, incl. on coordinate axes, by rotation, reflection, translation and enlargement (including fractional and negative scale factors)

Transformations

Worked answers, methods and verified real exam appearances for G7 on Edexcel GCSE Maths 1MA1.

Explanation

Describe a transformation completely: a translation needs a column vector; a rotation needs centre, angle and direction; a reflection needs its mirror line; an enlargement needs centre and scale factor. Translation, rotation and reflection preserve every length and angle, so object and image are congruent.
Enlargement preserves angles and multiplies every length from the centre by the scale factor. For centre $C$ , use $\overrightarrow{CP'}=k\overrightarrow{CP}$ .
A fractional factor shrinks the shape.
At Higher tier, a negative factor also puts every image point on the opposite side of the centre.
Examiners require every defining detail, not just the transformation name.

Corresponding points lie the same perpendicular distance from a reflection line.

Worked example

Point $P(5,1)$ is enlarged by scale factor $2$ about centre $C(2,3)$ . Find $P'$ .

1. $\overrightarrow{CP}=(5-2,1-3)=(3,-2)$ .
2.Multiply by $2$ : $\overrightarrow{CP'}=(6,-4)$ .
3.Add the centre: $P'=(2+6,3-4)=(8,-1)$ .

Answer: $P'=(8,-1)$ .

Common mistakes

Don't give 'rotation' without its centre, angle and direction, or 'reflection' without the mirror line.
Don't multiply the original coordinates by the scale factor even though the enlargement centre is not the origin.

Exam tip

For an enlargement, draw straight rays from the centre through corresponding points to check the centre and scale factor.

Worked practice

Tier 1 · Easy

Point

A(-3,4)

is translated by the vector

\begin{pmatrix}5\\-2\end{pmatrix}

. Find the coordinates of its image.

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$(2,2)$	2	Add the vector components to the coordinates: $(-3+5,4-2)=(2,2)$ .

Tier 2 · Standard

Point

P(4,-1)

is rotated

90^\circ

anticlockwise about the origin. Find the coordinates of its image

P'

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$P'(1,4)$	2	A $90^\circ$ anticlockwise rotation about the origin maps $(x,y)$ to $(-y,x)$ . Therefore $(4,-1)$ maps to $(1,4)$ .

Tier 3 · Hard

Triangle

ABC

has vertices

A(6,3)

B(0,5)

and

C(-2,-1)

. It is enlarged by scale factor

-\frac12

about centre

(2,-1)

. Find the three image coordinates.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$A'(0,-3)$ $B'(3,-4)$ $C'(4,-1)$	4	Subtract the centre, multiply by $-\frac12$ , then add the centre. For $A$ , $(4,4)\mapsto(-2,-2)$ , giving $(0,-3)$ . For $B$ , $(-2,6)\mapsto(1,-3)$ , giving $(3,-4)$ . For $C$ , $(-4,0)\mapsto(2,0)$ , giving $(4,-1)$ .

Tier 1 · Easy

Point

B(-4,3)

is reflected in the

y

-axis. Write down the coordinates of its image.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$(4,3)$	1	Reflection in the $y$ -axis changes the sign of the $x$ -coordinate and keeps the $y$ -coordinate, so $(-4,3)$ maps to $(4,3)$ .

Tier 2 · Standard

Point

C(5,-2)

is enlarged by scale factor

3

about the origin. Find the coordinates of its image.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$(15,-6)$	2	For an enlargement about the origin, multiply both coordinates by the scale factor: $(5\times3,-2\times3)=(15,-6)$ .

Tier 3 · Hard

Describe fully the single transformation that maps the triangle with vertices

(3,1)

(6,1)

and

(3,4)

to the triangle with vertices

(1,5)

(1,8)

and

(-2,5)

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	Rotation $90^\circ$ anticlockwise about $(0,2)$ (accept rotation $270^\circ$ clockwise about $(0,2)$ )	3	Relative to the centre $(0,2)$ , each vertex is rotated a quarter turn anticlockwise: the rule is $(x,y)\mapsto(2-y,\,x+2)$ , so $(3,1)\mapsto(1,5)$ , $(6,1)\mapsto(1,8)$ and $(3,4)\mapsto(-2,5)$ . Both triangles have the same orientation, so the transformation is a rotation; the centre $(0,2)$ is the fixed point of the vertex correspondences.

Tier 2 · Standard

Triangle

ABC

has vertices

A(-3,2)

B(1,5)

and

C(4,-2)

. The triangle is reflected in the line

y=x

. Find the coordinates of the three image vertices.

(2)

(Total for Question 7 is 2 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$A'(2,-3)$ $B'(5,1)$ $C'(-2,4)$	2	Reflection in $y=x$ swaps each point's coordinates. Therefore $(-3,2)\mapsto(2,-3)$ , $(1,5)\mapsto(5,1)$ and $(4,-2)\mapsto(-2,4)$ .

Tier 3 · Hard

An enlargement maps

A(2,1)

A'(5,3)

and

B(8,1)

B'(8,3)

. Describe the enlargement fully.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	Enlargement with centre $(8,5)$ and scale factor $\frac12$	4	The object length $AB$ is $6$ and the image length $A'B'$ is $3$ , so the scale factor is $\frac12$ . The centre lies on both $AA'$ and $BB'$ . Line $BB'$ is $x=8$ ; extending $AA'$ to meet it gives $(8,5)$ . Equivalently, for scale factor $\frac12$ , the centre is $2A'-A=(8,5)$ .

Tier 3 · Hard

A translation maps

A(-4,3)

A'(2,-2)

. Describe the translation fully. The same translation maps

B(1,4)

B'

C(-3,-2)

C'

, and

D

D'(0,6)

. Work out the coordinates of

B'

C'

and

D

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	Translation by $\begin{pmatrix}6\\-5\end{pmatrix}$ ; $B'=(7,-1)$ ; $C'=(3,-7)$ ; $D=(-6,11)$	4	The movement from $A$ to $A'$ is $(2-(-4),-2-3)=(6,-5)$ , so the translation vector is $\begin{pmatrix}6\\-5\end{pmatrix}$ . Adding it gives $B'=(1+6,4-5)=(7,-1)$ and $C'=(-3+6,-2-5)=(3,-7)$ . Subtracting the vector from $D'$ gives $D=(0-6,6-(-5))=(-6,11)$ .

Q10

Tier 3 · Hard

Higher only: An enlargement with scale factor

-2

maps

P(4,1)

P'(-5,7)

. Work out the centre of enlargement. The same enlargement maps

Q(-2,5)

Q'

. Work out the coordinates of

Q'

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	Centre $(1,3)$ ; $Q'=(7,-1)$	4	For centre $C$ , the rule is $P'=C-2(P-C)=3C-2P$ . Hence $3C=P'+2P=(-5,7)+(8,2)=(3,9)$ , so $C=(1,3)$ . From $C$ to $Q$ the vector is $(-3,2)$ . Multiplying it by $-2$ gives $(6,-4)$ , and adding this to $C$ gives $Q'=(7,-1)$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-06	1H	Q11	3	Non-calculator	Higher	QP MS
2022-06	1F	Q3	1	Non-calculator	Foundation	QP MS
2022-11	3F	Q18	2	Allowed	Foundation	QP MS
2024-11	2H	Q11	2	Allowed	Higher	QP MS
2024-06	1F	Q19	2	Non-calculator	Foundation	QP MS
2023-11	2F	Q21	2	Allowed	Foundation	QP MS
2023-06	3F	Q16	2	Allowed	Foundation	QP MS
2024-06	3F	Q18	3	Allowed	Foundation	QP MS
2023-11	1F	Q11	2	Non-calculator	Foundation	QP MS
2022-11	1H	Q11	2	Non-calculator	Higher	QP MS
2022-11	1F	Q11	4	Non-calculator	Foundation	QP MS
2024-11	1F	Q10	3	Non-calculator	Foundation	QP MS
2019-06	3H	Q8	2	Allowed	Higher	QP MS
2022-06	2F	Q22	2	Allowed	Foundation	QP MS
2019-11	3H	Q9	2	Allowed	Higher	QP MS
2022-06	2H	Q13	2	Allowed	Higher	QP MS
2022-06	2H	Q2	2	Allowed	Higher	QP MS
2019-06	1F	Q26	3	Non-calculator	Foundation	QP MS
2021-11	2F	Q11	2	Allowed	Foundation	QP MS
2023-06	2F	Q12	2	Allowed	Foundation	QP MS
2019-11	2F	Q13	2	Allowed	Foundation	QP MS
2024-06	3H	Q12	2	Allowed	Higher	QP MS
2021-11	3F	Q16	2	Allowed	Foundation	QP MS
2019-11	3F	Q18	2	Allowed	Foundation	QP MS
2019-06	1H	Q5	3	Non-calculator	Higher	QP MS
2024-11	2F	Q18	2	Allowed	Foundation	QP MS

Other points in G Geometry and measures

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