Cambridge IGCSE Maths (0580) · Topic 7: Transformations and vectors · 7.1
Transformations questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
The point \((3, -2)\) is translated by the vector \(\begin{pmatrix} -5 \\ 4 \end{pmatrix}\).
Find the coordinates of its image.
Answer: \((-2, 2)\)
The point \((4, 1)\) is reflected
(a) in the \(x\)-axis
(b) in the \(y\)-axis.
Find the coordinates of each image.
Answer: (a) \((4, -1)\) (b) \((-4, 1)\)
The point \((2, 5)\) is rotated about the origin. Write down its image after a rotation of
(a) \(90^\circ\) clockwise (b) \(180^\circ\).
Answer: (a) \((5, -2)\) (b) \((-2, -5)\)
The point \((2, 5)\) is rotated \(90°\) clockwise about the origin.
Find the coordinates of its image.
Answer: \((5, -2)\)
A triangle has corners \((1, 1)\), \((3, 1)\) and \((1, 2)\). It is enlarged by scale factor \(3\), centre the origin.
Find the coordinates of the corners of the image.
Answer: \((3, 3)\), \((9, 3)\) and \((3, 6)\)
The point \((6, 8)\) is enlarged by scale factor \(\frac{1}{2}\), centre \((2, 0)\).
Find the coordinates of its image.
Answer: \((4, 4)\)
A triangle has vertices \((1, 1)\), \((2, 1)\) and \((1, 3)\). It is enlarged with scale factor 3, centre the origin. Write down the vertices of the image.
Answer: \((3, 3), (6, 3), (3, 9)\)
The points \((4, 6)\) and \((8, 2)\) are enlarged with scale factor \(\frac{1}{2}\), centre the origin. Write down their images.
Answer: \((2, 3)\) and \((4, 1)\)
Triangle \(A\) has corners \((1, 2)\), \((3, 2)\) and \((3, 5)\). Triangle \(B\) has corners \((-1, 2)\), \((-3, 2)\) and \((-3, 5)\).
Describe fully the single transformation that maps \(A\) onto \(B\).
Answer: Reflection in the \(y\)-axis (\(x = 0\))
Extended content, for Papers 2 and 4. Core students can skip these.
The point \((5, -2)\) is reflected
(a) in the line \(y = x\)
(b) in the line \(y = -x\).
Find the coordinates of each image.
Answer: (a) \((-2, 5)\) (b) \((2, -5)\)
The point \((3, 2)\) is enlarged by scale factor \(-2\), centre \((1, 1)\).
Find the coordinates of its image.
Answer: \((-3, -1)\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Transformations is on both tiers (syllabus 7.1), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 7 (Transformations and vectors), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision