# A line segment has endpoints at (9 ,3 ) and (5 ,9 ). The line segment is dilated by a factor of 3  around (4 ,4 ). What are the new endpoints and length of the line segment?

Jul 27, 2018

color(brown)(A' (19,1), B' (7,18)

color(chocolate)("Length of the line segment after dilation "color(blue)(vec(A’B’) ~~ 21.6333

#### Explanation:

$A \left(9 , 3\right) , B \left(5 , 9\right) , C \left(64 , 4\right)$, dilation factor $3$

A’ = 3a - 2c

A’((x),(y)) = 3 * ((9),(3)) - 2 * ((4),(4))

A’((x),(y)) = ((19),(1))

B’((x),(y)) = 3 * ((5),(9)) - 2 * ((4),(4))

B’((x),(y)) = ((7),(19))

color(brown)("Length of the line segment after dilation "

color(blue)(vec(A’B’) = sqrt((19- 7)^2 + (1- 19)^2) ~~ 21.6333