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

##### 1 Answer
Jul 14, 2018

color(indigo)("New coordinates are " (7/5,1), (6/5,7/5), (6/5,2)

#### Explanation:

$A \left(3 , 1\right) , B \left(2 , 3\right) , C \left(2 , 6\right) , \text{ about point " D (1,1), " dilation factor } \frac{1}{5}$

$A ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\frac{1}{5}\right) a - \left(- \frac{4}{5}\right) d = \left(\frac{1}{5}\right) \cdot \left(\begin{matrix}3 \\ 1\end{matrix}\right) - \left(- \frac{4}{5}\right) \cdot \left(\begin{matrix}1 \\ 1\end{matrix}\right) = \left(\begin{matrix}\frac{7}{5} \\ 1\end{matrix}\right)$

$B ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\frac{1}{5}\right) b - \left(- \frac{4}{5}\right) d = \left(\frac{1}{5}\right) \cdot \left(\begin{matrix}2 \\ 3\end{matrix}\right) - \left(- \frac{4}{5}\right) \cdot \left(\begin{matrix}1 \\ 1\end{matrix}\right) = \left(\begin{matrix}\frac{6}{5} \\ \frac{7}{5}\end{matrix}\right)$

$C ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\frac{1}{5}\right) c - \left(- \frac{4}{5}\right) d = \left(\frac{1}{5}\right) \cdot \left(\begin{matrix}2 \\ 6\end{matrix}\right) - \left(- \frac{4}{5}\right) \cdot \left(\begin{matrix}1 \\ 1\end{matrix}\right) = \left(\begin{matrix}\frac{6}{5} \\ 2\end{matrix}\right)$

color(indigo)("New coordinates are " (7/5,1), (6/5,7/5), (6/5,2)