Question

A line segment has endpoints at `(7 ,3 )` and `(5 ,8 )`. The line segment is dilated by a factor of `3` around `(3 ,4 )`. What are the new endpoints and length of the line segment?

Answer 1

`color(purple)("New end points are " (15,1), (9,18)`

`color(crimson)("Length of the line segment " ~~ 18.0278`

Explanation:

`A(7,3), B(5,8), " about point " D (3,4), " dilation factor " 3`

`A'((x),(y)) =(3)a - (2)d =(3)* ((7),(3)) - (2)*((3),(4)) = ((15),(1))`

`B'((x),(y)) = (3)b - (2)d = (3)* ((5),(8)) - (2)*((3),(4)) = ((9),(18)`

`color(purple)("New end points are " (15,1), (9,18)`

`color(crimson)("Length of the line segment " = sqrt((15-9)^2 + (1-18)^2) ~~ 18.0278`