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

Jul 14, 2018

color(blue)("New coordinates are " (9/5, 8/5), (7/5,12/5), (13/5,18/5)

#### Explanation:

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

$A ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\frac{2}{5}\right) a - \left(- \frac{3}{5}\right) d = \left(\frac{2}{5}\right) \cdot \left(\begin{matrix}3 \\ 1\end{matrix}\right) - \left(- \frac{3}{5}\right) \cdot \left(\begin{matrix}1 \\ 2\end{matrix}\right) = \left(\begin{matrix}\frac{9}{5} \\ \frac{8}{5}\end{matrix}\right)$

$B ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\frac{2}{5}\right) b - \left(- \frac{3}{5}\right) d = \left(\frac{2}{5}\right) \cdot \left(\begin{matrix}2 \\ 3\end{matrix}\right) - \left(- \frac{3}{5}\right) \cdot \left(\begin{matrix}1 \\ 2\end{matrix}\right) = \left(\begin{matrix}\frac{7}{5} \\ \frac{12}{5}\end{matrix}\right)$

$C ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\frac{2}{5}\right) c - \left(- 35\right) d = \left(\frac{2}{5}\right) \cdot \left(\begin{matrix}5 \\ 6\end{matrix}\right) - \left(- \frac{3}{5}\right) \cdot \left(\begin{matrix}1 \\ 2\end{matrix}\right) = \left(\begin{matrix}\frac{13}{5} \\ \frac{18}{5}\end{matrix}\right)$

color(blue)("New coordinates are " (9/5, 8/5), (7/5,12/5), (13/5,18/5)