EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Translations and Combinations
Translations and combinations of different transformations · Transformations and constructions · Lesson 4 of 8 · 16 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 NON-CALCULATOR (2 marks)
Triangle A has vertices (1, 1), (1, 3) and (3, 1). It is translated by the vector beginpmatrix 4 \ −3 endpmatrix. Write down the coordinates of the vertices of the image.
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(Total for Question 1 = 2 marks)
Question 2 NON-CALCULATOR (2 marks)
The point P(2, 5) is mapped to P'(−1, 2) by a translation. Write the translation as a column vector.
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(Total for Question 2 = 2 marks)
Question 3 NON-CALCULATOR (4 marks)
The diagram shows triangles A, B and C. (a) Describe fully the single transformation that maps A onto B. (b) Describe fully the single transformation that maps B onto C.
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(Total for Question 3 = 4 marks)
Question 4 NON-CALCULATOR (3 marks)
Using the diagram in the last question, describe fully the single transformation that maps triangle A onto triangle C.
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(Total for Question 4 = 3 marks)
Question 5 NON-CALCULATOR (2 marks)
A shape is translated by beginpmatrix 3 \ 2 endpmatrix and then by beginpmatrix −5 \ 4 endpmatrix. Write down the single translation that does the same job.
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(Total for Question 5 = 2 marks)
Question 6 NON-CALCULATOR (3 marks)
The shape P is reflected in the line x = 1 and then the image is reflected in the line x = 4. Describe fully the single transformation that is equivalent to these two reflections.
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
(5, −2), (5, 0) and (7, −2).
• Two vertices correct B1
• All three correct B1
Question 2 (2 marks)
beginpmatrix −3 \ −3 endpmatrix.
• One number correct M1
• Both correct A1
Question 3 (4 marks)
(a) A reflection in the y-axis (the line x = 0). (b) A reflection in the x-axis (the line y = 0).
• (a) Reflection B1
• (a) The y-axis, or x = 0 B1
• (b) Reflection B1
• (b) The x-axis, or y = 0 B1
Question 4 (3 marks)
A rotation of 180° about the origin (0, 0).
• Rotation B1
• 180° B1
• Centre (0, 0) B1
Question 5 (2 marks)
Add the vectors: beginpmatrix 3 + (−5) \ 2 + 4 endpmatrix = beginpmatrix −2 \ 6 endpmatrix.
• Adding the vectors M1
• beginpmatrix −2 \ 6 endpmatrix A1
Question 6 (3 marks)
A translation by beginpmatrix 6 \ 0 endpmatrix: twice the distance between the mirror lines (2 × 3 = 6) to the right.
• Translation B1
• Distance 6 (twice the gap between the lines) M1
• beginpmatrix 6 \ 0 endpmatrix A1