Karen Morrison and Nick Hamshaw Solutions for Exercise 10: Examination practice

In each case , describe fully the transformation that maps $A$ onto: $B, C \& D$ and state which shapes have an area equal to that of $A$.

If $\overrightarrow{AB} = \left(\begin{array}{c}-3\\ 5\end{array}\right)$, then $\left|\overrightarrow{AB}\right|=\sqrt{k}$. Find the value of $k$.

Describe fully the single transformation that maps.

shape $A$ onto shape $B$

Describe fully the single transformation that maps.

shape $A$ onto shape $C$

Describe fully the single transformation that maps.

shape $A$ onto shape $D$

Draw the image of shape $A$ after a translation by vector $\left(\begin{array}{c}2\\ -3\end{array}\right)$

The diagram shows a quadrilateral $OABC$. $\stackrel{\rightharpoonup }{OA}=a, \stackrel{\rightharpoonup }{OC}=c$ and $\stackrel{\rightharpoonup }{CB}=2a$. $X$ is a point on $OB$ such that $OX:XB=1:2$. Find $\stackrel{\rightharpoonup }{AC}$ and $\stackrel{\rightharpoonup }{AX}$ in terms of $a$ and $c,$ in its simplest form

The diagram shows a quadrilateral $OABC$. $\stackrel{\rightharpoonup }{OA}=a, \stackrel{\rightharpoonup }{OC}=c$ and $\stackrel{\rightharpoonup }{CB}=2a$. $X$ is a point on $OB$ such that $OX:XB=1:2$. Explain why the vectors $\stackrel{\rightharpoonup }{AC}$ and $\stackrel{\rightharpoonup }{AX}$ show that $C, X$ and $A$ lie on a straight line.