\question[2]
How to find the scale factor
\vspace{2mm}

a) Find a side on the original shape that is easy to describe e.g. 2 right, 1 up

b) Describe how to draw the matching side on the large shape e.g. 6 right, 3 up

c) Find the scale factor $\Box$, that is $2 \times \Box = 6$ or $1 \times \Box = 3$

\begin{tikzpicture}[scale = 0.4]
\draw[xstep= 1cm, ystep=1cm, semithick](-0.01,-0.01) grid (16.01,10.01);
\draw[ultra thick, >=latex, ->](-1, 0) --(17.75, 0) node[right] {$x$} coordinate(x axis);
\draw[ultra thick, >=latex, ->](0, 0) --(0, 11.5) node[above] {$y$} coordinate(y axis);
\small
\foreach \x in {2, 4, ..., 16 } \node at (\x,-0.7) [fill=white] {$\x$};
\foreach \y in { 2, 4, ..., 10 }\node at (-0.9,\y) [fill=white] {$\y$};
%\node [fill=white, shift={(-0.3, -0.3)}] at (0,0) {$\textit{O}$};
\normalsize
\foreach \sf in {1}
\draw[ultra thick] (4,3)--++(\sf*2,\sf*-1)--++(\sf*1,\sf*1)--++(\sf*-1,\sf*1);%--cycle;
\node at (5.5,3) {\textbf{A}};
\foreach \sf in {3}
\draw[ultra thick] (6,5)--++(\sf*2,\sf*-1)--++(\sf*1,\sf*1)--++(\sf*-1,\sf*1);%--cycle;
\node at (10.5,5) {\textbf{B}};
\foreach \sf in {1}
\draw[ultra thick, dashed, ->] (4,3)--++(\sf*2,\sf*1);
\foreach \sf in {3}
\draw[ultra thick, dashed,->] (6,5)--++(\sf*2,\sf*1);
\end{tikzpicture}

\question[2]
How to find the centre of enlargement
\vspace{2mm}

a) Join up two matching corners* \hspace {2cm} (b) ... and two more matching corners* 

\begin{tikzpicture}[scale = 0.4]
\draw[xstep= 1cm, ystep=1cm, semithick](-0.01,-0.01) grid (16.01,10.01);
\draw[ultra thick, >=latex, ->](-1, 0) --(17.75, 0) node[right] {$x$} coordinate(x axis);
\draw[ultra thick, >=latex, ->](0, 0) --(0, 11.5) node[above] {$y$} coordinate(y axis);
\node at (6,2) {$\blacksquare$};\node at (12,2) {$\blacksquare$};
\small
\foreach \x in {2, 4, ..., 16 } \node at (\x,-0.7) [fill=white] {$\x$};
\foreach \y in { 2, 4, ..., 10 }\node at (-0.9,\y) [fill=white] {$\y$};
%\node [fill=white, shift={(-0.3, -0.3)}] at (0,0) {$\textit{O}$};
\normalsize
\foreach \sf in {1}
\draw[ultra thick] (4,3)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (5.5,3) {\textbf{A}};
\foreach \sf in {3}
\draw[ultra thick] (6,5)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (10.5,5) {\textbf{B}};
\draw [ultra thick, dashed] (16,2)--(0,2);
\end{tikzpicture}
\begin{tikzpicture}[scale = 0.4]
\draw[xstep= 1cm, ystep=1cm, semithick](-0.01,-0.01) grid (16.01,10.01);
\draw[ultra thick, >=latex, ->](-1, 0) --(17.75, 0) node[right] {$x$} coordinate(x axis);
\draw[ultra thick, >=latex, ->](0, 0) --(0, 11.5) node[above] {$y$} coordinate(y axis);
\node at (7,3) {$\blacksquare$};\node at (15,5) {$\blacksquare$};
\small
\foreach \x in {2, 4, ..., 16 } \node at (\x,-0.7) [fill=white] {$\x$};
\foreach \y in { 2, 4, ..., 10 }\node at (-0.9,\y) [fill=white] {$\y$};
%\node [fill=white, shift={(-0.3, -0.3)}] at (0,0) {$\textit{O}$};
\normalsize
\foreach \sf in {1}
\draw[ultra thick] (4,3)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (5.5,3) {\textbf{A}};
\foreach \sf in {3}
\draw[ultra thick] (6,5)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (10.5,5) {\textbf{B}};
\draw [ultra thick, dashed] (16,2)--(0,2);\draw [thick, dotted] (16,5.25)--(0,1.25);
\end{tikzpicture}

c) ... and two more matching corners* (just to be sure) \hspace {1mm} (d) ... and the last if you like* 

\begin{tikzpicture}[scale = 0.4]
\draw[xstep= 1cm, ystep=1cm, semithick](-0.01,-0.01) grid (16.01,10.01);
\draw[ultra thick, >=latex, ->](-1, 0) --(17.75, 0) node[right] {$x$} coordinate(x axis);
\draw[ultra thick, >=latex, ->](0, 0) --(0, 11.5) node[above] {$y$} coordinate(y axis);
\node at (4,3) {$\blacksquare$};\node at (6,5) {$\blacksquare$};
\small
\foreach \x in {2, 4, ..., 16 } \node at (\x,-0.7) [fill=white] {$\x$};
\foreach \y in { 2, 4, ..., 10 }\node at (-0.9,\y) [fill=white] {$\y$};
%\node [fill=white, shift={(-0.3, -0.3)}] at (0,0) {$\textit{O}$};
\normalsize
\foreach \sf in {1}
\draw[ultra thick] (4,3)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (5.5,3) {\textbf{A}};
\foreach \sf in {3}
\draw[ultra thick] (6,5)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (10.5,5) {\textbf{B}};
\draw [ultra thick, dashed] (16,2)--(0,2);\draw [thick, dotted] (11,10)--(1,0);
 \draw [thick, dotted] (16,5.25)--(0,1.25);
\end{tikzpicture}
\begin{tikzpicture}[scale = 0.4]
\draw[xstep= 1cm, ystep=1cm, semithick](-0.01,-0.01) grid (16.01,10.01);
\draw[ultra thick, >=latex, ->](-1, 0) --(17.75, 0) node[right] {$x$} coordinate(x axis);
\draw[ultra thick, >=latex, ->](0, 0) --(0, 11.5) node[above] {$y$} coordinate(y axis);
\node at (6,4) {$\blacksquare$};\node at (12,8) {$\blacksquare$};
\small
\foreach \x in {2, 4, ..., 16 } \node at (\x,-0.7) [fill=white] {$\x$};
\foreach \y in { 2, 4, ..., 10 }\node at (-0.9,\y) [fill=white] {$\y$};
%\node [fill=white, shift={(-0.3, -0.3)}] at (0,0) {$\textit{O}$};
\normalsize
\foreach \sf in {1}
\draw[ultra thick] (4,3)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (5.5,3) {\textbf{A}};
\foreach \sf in {3}
\draw[ultra thick] (6,5)--++(\sf*2,\sf*1)--++(\sf*1,\sf*-1)--++(\sf*-1,\sf*-1)--cycle;
\node at (10.5,5) {\textbf{B}};
\draw [ultra thick, dashed] (16,2)--(0,2);\draw [thick, dotted] (11,10)--(1,0);
\draw [thick, dashed] (15,10)--(0,0); \draw [thick, dotted] (16,5.25)--(0,1.25);
\end{tikzpicture}

\hspace{5cm}* with a line which goes from one side of the grid to the other

The point where all the lines join (3, 2) is the centre of enlargement

\question[3]
Describe fully the transformation that maps shape A onto shape B (3 things)

(i) ``enlargement" (ii)  ``scale factor"  = 3 (iii) ``centre" (3, 2)