# A triangle has corners at (3, 4 ), ( 6, 3 ), and ( 7 , 2 ). If the triangle is dilated by  5 x around (1, 1), what will the new coordinates of its corners be?

Nov 25, 2017

(11,16),(26,11)" and "((31,6)

#### Explanation:

$\text{let the points be A, B and C and their images A', B' and C'}$

$\text{let the centre of dilatation be } D \left(1 , 1\right)$

$\vec{D A '} = \textcolor{red}{5} \vec{D A} = 5 \left(\underline{a} - \underline{d}\right)$

$= 5 \left[\left(\begin{matrix}3 \\ 4\end{matrix}\right) - \left(\begin{matrix}1 \\ 1\end{matrix}\right)\right] = 5 \left(\begin{matrix}2 \\ 3\end{matrix}\right) = \left(\begin{matrix}10 \\ 15\end{matrix}\right)$

$\Rightarrow A ' = \left(1 + 10 , 1 + 15\right) = \left(11 , 16\right)$

$\vec{D B '} = \textcolor{red}{5} \vec{D B} = 5 \left(\underline{b} - \underline{d}\right)$

$= 5 \left[\left(\begin{matrix}6 \\ 3\end{matrix}\right) - \left(\begin{matrix}1 \\ 1\end{matrix}\right)\right] = 5 \left(\begin{matrix}5 \\ 2\end{matrix}\right) = \left(\begin{matrix}25 \\ 10\end{matrix}\right)$

$\Rightarrow B ' = \left(1 + 25 , 1 + 10\right) = \left(26 , 11\right)$

$\vec{D C '} = \textcolor{red}{5} \vec{D C} = 5 \left(\underline{c} - \underline{d}\right)$

$= 5 \left[\left(\begin{matrix}7 \\ 2\end{matrix}\right) - \left(\begin{matrix}1 \\ 1\end{matrix}\right)\right] = 5 \left(\begin{matrix}6 \\ 1\end{matrix}\right) = \left(\begin{matrix}30 \\ 5\end{matrix}\right)$

$\Rightarrow C ' = \left(30 + 1 , 5 + 1\right) = \left(31 , 6\right)$