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Cambridge IGCSE Maths: Transformations and vectors — Practice Questions & Answers
A complete guide to the four IGCSE transformations (translation, reflection, rotation, enlargement), how to describe each one fully, how to combine them, and how column vectors, position vectors, magnitude and vector geometry tie the whole topic together.
58 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
The point $P(3,4)$ is translated by the column vector $\binom{2}{-1}$. What are the coordinates of the image?
$(5,3)$
$(1,5)$
$(5,5)$
$(6,-4)$
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Why Add the vector to the coordinates: $(3+2, 4+(-1)) = (5,3)$.
2
Multiple choice · Easy
Which column vector translates the point $(1,2)$ to the point $(4,6)$?
$\binom{3}{4}$
$\binom{4}{6}$
$\binom{-3}{-4}$
$\binom{5}{8}$
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Why The translation vector is found by subtracting: $\binom{4-1}{6-2} = \binom{3}{4}$.
3
Multiple choice · Easy
The point $(5,2)$ is reflected in the $x$-axis. What is the image?
$(5,-2)$
$(-5,2)$
$(-5,-2)$
$(2,5)$
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Why Reflection in the $x$-axis keeps $x$ the same and negates $y$: $(5,-2)$.
4
Multiple choice · Easy
What is the result of $\binom{2}{5} + \binom{3}{-1}$?
$\binom{5}{4}$
$\binom{5}{6}$
$\binom{-1}{6}$
$\binom{6}{-5}$
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Why Add the components separately: $\binom{2+3}{5+(-1)} = \binom{5}{4}$.
5
Multiple choice · Easy
What is the result of $3\binom{2}{-4}$?
$\binom{6}{-12}$
$\binom{5}{-1}$
$\binom{6}{-4}$
$\binom{6}{12}$
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Why Multiply each component by $3$: $\binom{6}{-12}$.
6
Multiple choice · Easy
A shape is enlarged by scale factor $2$. The original has an area of $5$ square units. What is the area of the image?
$20$ square units
$10$ square units
$7$ square units
$25$ square units
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Why Area scales by the square of the scale factor: $5 \times 2^{2} = 5 \times 4 = 20$.
7
Multiple choice · Easy
The point $(2,3)$ is enlarged with centre the origin and scale factor $3$. What is the image?
$(6,9)$
$(5,6)$
$(6,3)$
$(2,9)$
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Why Multiply each coordinate by the scale factor about the origin: $(2\times3, 3\times3) = (6,9)$.
8
Multiple choice · Medium
The point $(4,1)$ is reflected in the line $y=x$. What is the image?
$(1,4)$
$(-4,-1)$
$(4,-1)$
$(-1,-4)$
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Why Reflection in $y=x$ swaps the coordinates: $(1,4)$.
9
Multiple choice · Hard
The point $(2,5)$ is reflected in the line $y=-x$. What is the image?
$(-5,-2)$
$(5,2)$
$(-2,-5)$
$(5,-2)$
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Why Reflection in $y=-x$ swaps the coordinates and negates both: $(-5,-2)$.
10
Multiple choice · Medium
The point $(3,2)$ is rotated $90$ degrees anticlockwise about the origin. What is the image?
$(-2,3)$
$(2,-3)$
$(-3,-2)$
$(2,3)$
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Why A $90$ degree anticlockwise rotation about the origin maps $(x,y)$ to $(-y,x)$: $(-2,3)$.
Key terms in Transformations and vectors
Transformation: A change in the position, size, or orientation of a shape.
Object: The original shape before a transformation is applied.
Image: The resulting shape after a transformation is applied.
Translation: A transformation that slides a shape without rotating or reflecting it.
Column vector: A vector written vertically as $\begin{pmatrix} x \\ y \end{pmatrix}$ describing a movement.
Reflection: A transformation that flips a shape across a mirror line.
Mirror line: The line across which a shape is reflected.
Line of reflection: The fixed line acting as a mirror in a reflection.
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