Question

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?

Answer 1

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

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

Explanation:

`A(8,4), B(2,3), " about point " D (3,2), " dilation factor "3`

`A'((x),(y)) =(3)a - (2)d =(3)*((8),(4)) - (2)*((3),(2)) = ((18),(8))`

`B'((x),(y)) = (3)b - (2)d = (3)*((3),(7)) - (2)*((3),(2)) = ((3),(17))`

`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`