# A line segment has endpoints at (8 ,4 ) and (3 ,7 ). The line segment is dilated by a factor of 3  around (3 ,2 ). What are the new endpoints and length of the line segment?

Jul 14, 2018

color(chocolate)("New coordinates are " (18,8), (3,17)

color(chocolate)("Length of the line segment " ~~ 17.4929

#### Explanation:

$A \left(8 , 4\right) , B \left(2 , 3\right) , \text{ about point " D (3,2), " dilation factor } 3$

$A ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(3\right) a - \left(2\right) d = \left(3\right) \cdot \left(\begin{matrix}8 \\ 4\end{matrix}\right) - \left(2\right) \cdot \left(\begin{matrix}3 \\ 2\end{matrix}\right) = \left(\begin{matrix}18 \\ 8\end{matrix}\right)$

$B ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(3\right) b - \left(2\right) d = \left(3\right) \cdot \left(\begin{matrix}3 \\ 7\end{matrix}\right) - \left(2\right) \cdot \left(\begin{matrix}3 \\ 2\end{matrix}\right) = \left(\begin{matrix}3 \\ 17\end{matrix}\right)$

color(chocolate)("New coordinates are " (18,8), (3,17)

color(chocolate)("Length of the line segment '" = sqrt((18-3)^2 + (8-17)^2) ~~ 17.4929