Mathematics 4024 · O Level · Vectors in two dimensions

Vectors in two dimensions — practice question

ABCDE is a pentagon. $AFB$, $AHE$ and $BGC$ lie on straight lines.
(a(i))[1]

$\vec{AE} = \begin{pmatrix}6\\1\end{pmatrix}$. Calculate $|\vec{AE}|$.

(a(ii))[2]

$H$ is the midpoint of $AE$, and $\vec{FH} = \begin{pmatrix}2\\-3.5\end{pmatrix}$. Find $\vec{AF}$.

(a(iii)(a))[1]

$G$ divides $BC$ in the ratio $1 : 2$. $\vec{BG} = \begin{pmatrix}2.5\\0\end{pmatrix}$ and $\vec{CD} = \begin{pmatrix}-1\\-7\end{pmatrix}$. Find $\vec{GD}$.

(a(iii)(b))[1]

Explain why $GD$ is parallel to $FH$.

(a(iv))[1]

$B$ is the point $(3, 10)$. Find the coordinates of $D$.

(b(i))[1]

Flag $A$ is mapped onto flag $T$ by the translation $\begin{pmatrix}-3\\-6\end{pmatrix}$. Draw, and label, flag $T$.

(b(ii))[2]

Describe fully the enlargement that will map flag $A$ onto flag $B$.

(b(iii))[1]

Find the centre of the rotation that will map flag $A$ onto flag $C$.

(b(iv))[2]

Rotate flag $B$ through $45^{\circ}$ anticlockwise about the origin. Label the image $R$.

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