[tex]\bf \begin{array}{lllllll}
(&-9,&2),(&-10,&9)\\
&x_1&y_1&x_2&y_2
\end{array}\implies \ \textless \ x_2-x_1\ ,\ y_2-y_1\ \textgreater \ \leftarrow
\begin{array}{llll}
component\\
form
\end{array}
\\\\\\
\ \textless \ -10-(-9)\ ,\ 9-2\ \textgreater \ \implies \ \textless \ -1,7\ \textgreater \ \impliedby PQ\\\\
-------------------------------\\\\
2PQ\implies 2\ \textless \ -1,7\ \textgreater \ \implies \ \textless \ 2\cdot -1,2\cdot 7\ \textgreater \ \implies
\begin{array}{rllll}
\ \textless \ -2&,&14\ \textgreater \ \\
a&&b
\end{array}
\\\\\\
magnitude\qquad \sqrt{a^2+b^2}\implies \sqrt{(-2)^2+(14)^2}\implies \sqrt{200}
\\\\\\
10\sqrt{2}[/tex]
