Transformations and Vectors

Work out $3\mathbf{a} - \mathbf{b}$.

______

Find $|\mathbf{a} + \mathbf{b}|$.

______

Triangle $A$ is mapped onto triangle $P$ by a translation of $\begin{pmatrix} 1 \\ -3 \end{pmatrix}$.

Draw triangle $P$.

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

______

Transformation $\mathbf{M}$ is a reflection in the line $y = -1$.
Transformation $\mathbf{R}$ is a rotation $90°$ clockwise about $(1, 1)$.
$\mathbf{RM}(B) = Q$.

Draw triangle $Q$.

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

______

Find the coordinates of the centre of the enlargement.

( ______ , ______ )

Find the area of shape $C$.

______ $\text{units}^2$

On the grid, draw shape $D$.

Describe fully the single transformation represented by the matrix

______

$F$ is the point $(6, 1)$, $G$ is the point $(-2, 4)$ and $\overrightarrow{GH} = \begin{pmatrix} -1 \\ -8 \end{pmatrix}$.

Calculate $|\overrightarrow{FH}|$.

$|\overrightarrow{FH}|$ = ______

Write $\overrightarrow{OX}$ in terms of $m$, $k$, $\mathbf{a}$ and $\mathbf{b}$.

$\overrightarrow{OX}$ = ______

$\overrightarrow{BX} = \frac{3}{5}\mathbf{a} - \frac{1}{2}\mathbf{b}$

Find the value of $k$.

$k$ = ______

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

______

Find the matrix representing the transformation that maps triangle $A$ onto triangle $C$.

______

Triangle $A$ is mapped onto triangle $D$ by an enlargement with centre $(2, 3)$ and scale factor 3.

Draw triangle $D$.

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

______

Reflect shape $A$ in the $x$-axis.

Enlarge shape $A$ by scale factor 2, centre $(5, 4)$.

Draw and label shape $C$.

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

______

Find the matrix representing the transformation that maps shape $C$ onto shape $A$.

______

Reflect triangle $A$ in the line $x = 1$.

Label the image $B$.

Triangle $A$ is mapped onto triangle $D$ by a combination of two transformations.
Triangle $A$ is first mapped onto triangle $C$ by transformation $Y$.

Triangle $C$ is then mapped onto triangle $D$ by a translation of $\begin{pmatrix}6 \\ 1\end{pmatrix}$.

Describe fully transformation $Y$.

______

Calculate $|\overrightarrow{AB}|$.

$|\overrightarrow{AB}|$ = ______

Find the coordinates of the point $A$.

( ______ , ______ )

$B$ is the midpoint of $AD$.

Find the coordinates of the point $D$.

( ______ , ______ )

$\overrightarrow{PQ}$,

$\overrightarrow{PQ}$ = ______

$\overrightarrow{OS}$,

$\overrightarrow{OS}$ = ______

$\overrightarrow{SR}$.

$\overrightarrow{SR}$ = ______

Find $\overrightarrow{AB}$.

$\overrightarrow{AB}$ = ______

$\overrightarrow{BC} = \begin{pmatrix} -4 \\ 3 \end{pmatrix}$

Find the coordinates of $C$.

( ______ , ______ )

$|\overrightarrow{AD}| = \sqrt{74}$ and $D = (-3, n)$.

Find the possible values of $n$.

$n$ = ______ or $n$ = ______

$OQRP$ is a parallelogram.
$\overrightarrow{OP} = \mathbf{p}$ and $\overrightarrow{OQ} = \mathbf{q}$.
$K$ is the midpoint of $OQ$ and $L$ is a point on $PR$.
$\overrightarrow{KL} = \mathbf{p} - \frac{1}{10}\mathbf{q}$.

Find $PL : LR$.

______ : ______