CAIE IGCSE Mathematics Transformations and Vectors

Practise reflections, rotations, enlargements, translations and vector calculations across coordinate grids and geometric proofs.

Covered syllabus points

E7.1 Transformations E7.2 Vectors in two dimensions E7.3 Magnitude of a vector E7.4 Vector geometry

[Maximum number: 7]

(a)

A is the point (3,7) and B is the point (-1,5).

[ 3 ]

(i)

Write $\overrightarrow{A B}$ as a column vector.

()

[ 1 ]

$\begin{pmatrix}-4\\-2\end{pmatrix}$

(ii)

$\overrightarrow{A C}=3 \overrightarrow{B A}$

Find the coordinates of C.

[ 2 ]

(15,13)
FT their (a)(ii)
M1 for $\begin{pmatrix}12\\6\end{pmatrix}$ or $\begin{pmatrix}-12\\-6\end{pmatrix}$ seen
or for -1+16 and 5+8 seen

(b)

Figure for Question (b) — CAIE IGCSE Mathematics Extended

[ 4 ]

(i)

Rotate shape P through $180^{\circ}$ about the point (4,1).

[ 2 ]

Image at (4,1), (5,-1), (7,-1), (7,1)
B1 for rotation $180^\circ$ but incorrect position

(ii)

Reflect shape P in the line y=x+2.

[ 2 ]

[Maximum number: 5]

F is the point (1,-4), $\overrightarrow{FG}=\binom{8}{-3}$ and $\overrightarrow{GH}=\binom{-12}{35}$ .
Find

(a)

$3\overrightarrow{FG}$

[ 1 ]

$\binom{24}{-9}$

(b)

$\overrightarrow{F G}+\overrightarrow{G H}$

[ 1 ]

$\binom{-4}{32}$

(c)

the coordinates of the point G

[ 1 ]

(d)

the magnitude of vector $\overrightarrow{G H}$ .

[ 2 ]

37
M1 for $(-12)^2+35^2$ oe

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Covered syllabus points

7. Transformations and vectors question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

7. Transformations and vectors question 2

Question (a)

Question (b)

Question (c)

Question (d)