Transformations and Vectors

Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

______

Draw the image of triangle $A$ after a reflection in the line $x = -1$.

Find the value of $k$.

$k$ = ______

Find the coordinates of the other two vertices of triangle $C$.

( ______ , ______ ) and ( ______ , ______ )

Find $\overrightarrow{AX}$.
Give your answer in its simplest form in terms of $\mathbf{a}$ and $\mathbf{b}$.

$\overrightarrow{AX}$ = ______

Find $\overrightarrow{XC}$.
Give your answer in its simplest form in terms of $\mathbf{a}$ and $\mathbf{b}$.

$\overrightarrow{XC}$ = ______

The position vector of point $Q$ is $\begin{pmatrix} 2 \\ 5 \end{pmatrix}$.

Find the position vector of point $P$.

$\overrightarrow{OP}$ = ______

$|\overrightarrow{PQ}| = \sqrt{a}$

Find the value of $a$.

$a$ = ______

$\overrightarrow{AB}$

$\overrightarrow{AB}$ = ______

$\overrightarrow{OC}$.

$\overrightarrow{OC}$ = ______

$X$ is the point on $OC$ such that $OX : XC = 4 : 1$.

Find $\overrightarrow{BX}$.
Give your answer in its simplest form in terms of $\mathbf{a}$ and $\mathbf{b}$.

$\overrightarrow{BX}$ = ______

Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

______

Draw the image of triangle $A$ after a rotation of $180^\circ$ about centre $(0, 0)$.

Find $\overrightarrow{AB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

$\overrightarrow{AB}$ = ______

Show that the position vector of $T$ is $\frac{2}{5}(\mathbf{a} + 6\mathbf{b})$.

$Q$ is a point on $OB$ and $\overrightarrow{QT} = \frac{1}{5}(2\mathbf{a} - 3\mathbf{b})$.

Find $OQ : QB$.

______ : ______

Describe fully the single transformation that maps shape $A$ onto shape $B$.

______

Draw the image of shape $A$ after a rotation of $90^\circ$ clockwise about the origin.

$\overrightarrow{MQ}$

$\overrightarrow{MQ}$ = ______

$\overrightarrow{NM}$

$\overrightarrow{NM}$ = ______

Line $OP$ is extended to point $X$.
$MNX$ is a straight line.

Find the position vector of $X$.

______

$\overrightarrow{HK}$

$\overrightarrow{HK}$ = ______

$\overrightarrow{CD}$

$\overrightarrow{CD}$ = ______

$\overrightarrow{ML}$

$\overrightarrow{ML}$ = ______