Combined Transformations: GCSE and IGCSE Maths Practice
Transformations
Combined Transformations
24 self-marking GCSE and IGCSE practice questions on Combined Transformations, written specifically for AQA, Pearson, OCR, Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Instant marking with full worked solutions on every question.
A few of the 24 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 11 markGrade 1-3
Shape P is reflected in the line y=−1 to give shape Q.
One vertex of P, at (-2, -1), lies exactly on the mirror line.
Write down the coordinates of the point on P that is invariant under this reflection.
Show the worked solution
A point is invariant under a transformation if it maps to itself. Under a reflection, only points exactly on the mirror line do not move. Since the mirror line is y=−1, the invariant point is the vertex already on that line: (-2, -1).
What are the common mistakes in Combined Transformations?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Describes a combined transformation as a single reflection
Two reflections in perpendicular lines combine to give a rotation, not another reflection - check the overall effect on the coordinates (both signs reversed = 180° rotation).
Applies the reflection before the translation when the combined transformation requires the opposite order
Applied the reflection to the original shape instead of to the translated shape, ignoring the required order of the two transformations.
Wrongly moves a point that should stay invariant under the reflection
A point already on the mirror line does not move - it stays at its original coordinates; it is not reflected like the rest of the shape.
Quick answers about Combined Transformations
How many Combined Transformations practice questions are there?
There are 24 self-marking GCSE and IGCSE Maths questions on Combined Transformations, written for AQA, Pearson, OCR, Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Combined Transformations?
No. You can start practising Combined Transformations straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
Question 21 markGrade 4-6
Shape P has a vertex at (2, 3).
Shape P is first translated by the vector (−32) to give shape Q. Shape Q is then translated by the vector (24) to give shape R.
The corresponding vertex on R is at (1, 9).
Describe fully the single transformation that maps shape P directly onto shape R.
Show the worked solution
Combining two translations means adding the vectors: (−32)+(24)=(−16)
Question 32 marksGrade 6
Shape T is reflected in the line x = −1 to give shape R. Shape R is reflected in the line y = 1 to give shape S.
Describe the single transformation that will map shape T to shape S.
Question 43 marksGrade 6-7
Shape P has vertices (3, 1), (5, 1), (3, 4). Shape P is first translated by the vector (4−2), then reflected in the y-axis, to give shape Q.
Find the coordinates of the vertices of shape Q.
Question 55 marksGrade 6-7
Shape A has vertices P (3, 2), Q (6, 2), R (3, 5). Shape A is first translated by the vector (−30), then reflected in the x-axis, to give shape B.
(a)(i) Find the coordinates of P'.
(a)(ii) Find the coordinates of Q'.
(a)(iii) Find the coordinates of R'.
(b) Is there any point that maps to itself under this combined transformation? Explain your answer.
Question 61 markGrade 7-8
Triangle P has a vertex at (1, 2).
Triangle P is first reflected in the x-axis to give triangle Q. Triangle Q is then reflected in the y-axis to give triangle R.
The corresponding vertex on R is at (-1, -2).
Describe fully the single transformation that maps triangle P directly onto triangle R.