# A line segment has endpoints at (4 ,3 ) and (2 ,5 ). The line segment is dilated by a factor of 4  around (3 ,3 ). What are the new endpoints and length of the line segment?

Jul 14, 2018

color(purple)("New coordinates are " (7, 3), (-1, 11)

color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137

#### Explanation:

$A \left(8 , 4\right) , B \left(4 , 3\right) , \text{ about point " D (1,3), " dilation factor } 4$

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

$B ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(4\right) b - \left(3\right) d = \left(4\right) \cdot \left(\begin{matrix}2 \\ 5\end{matrix}\right) - \left(3\right) \cdot \left(\begin{matrix}3 \\ 3\end{matrix}\right) = \left(\begin{matrix}- 1 \\ 11\end{matrix}\right)$

color(purple)("New coordinates are " (7, 3), (-1, 11)

color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137