# A line segment has endpoints at (9 ,2 ) and (7 , 4). The line segment is dilated by a factor of 4  around (1 , 5). What are the new endpoints and length of the line segment?

Jul 14, 2018

color(orange)("New coordinates are " (33,-7), (-25, 1)

color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137

#### Explanation:

$A \left(8 , 4\right) , B \left(9 , 2\right) , \text{ about point " D (1,5), " dilation factor } 4$

$A ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(4\right) a - \left(3\right) d = \left(4\right) \cdot \left(\begin{matrix}9 \\ 2\end{matrix}\right) - \left(3\right) \cdot \left(\begin{matrix}1 \\ 5\end{matrix}\right) = \left(\begin{matrix}33 \\ - 7\end{matrix}\right)$

$B ' \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(4\right) b - \left(3\right) d = \left(4\right) \cdot \left(\begin{matrix}7 \\ 4\end{matrix}\right) - \left(3\right) \cdot \left(\begin{matrix}1 \\ 5\end{matrix}\right) = \left(\begin{matrix}25 \\ 1\end{matrix}\right)$

color(orange)("New coordinates are " (33,-7), (-25, 1)

color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137