Question

A line segment has endpoints at `(1 ,4 )` and `(3 ,5 )`. The line segment is dilated by a factor of `6` around `(2 ,5 )`. What are the new endpoints and length of the line segment?

Answer 1

`color(green)("New end points are " (-4,-1), (8,5)`

`color(green)("Length of the line segment " ~~ 13.4164`

Explanation:

`A(1,4), B(3,5), " about point " D (2,5), " dilation factor " 6`

`A'((x),(y)) =(6)a - (5)d =(6)* ((1),(4)) - (5)*((2),(5)) = ((-4),(-1))`

`B'((x),(y)) = (6)b - (5)d = (6)* ((3),(5)) - (5)*((2),(5)) = ((8),(5)`

`color(green)("New end points are " (-4,-1), (8,5)`

`color(green)("Length of the line segment " = sqrt((-4-8)^2 + (-1-5)^2) ~~ 13.4164`