Question

A line segment has endpoints at `(1 ,6 )` and `(6 ,7 )`. The line segment is dilated by a factor of `4` around `(4 ,3 )`. What are the new endpoints and length of the line segment?

Answer 1

`(1,6) to (-8,15)`

`(6,7) to (12, 19)`

`l = 4 sqrt{26}`

Explanation:

I did the general case [here.](https://socratic.org/questions/a-line-segment-has-endpoints-at-2-4-and-5-3-the-line-segment-is-dilated-by-a-fac-1#604871)

`(p,q)=(4,3), quad r=4, quad (a,b)=(1,6), quad (c,d)=(6,7)`

`(a,b) to ( (1-r)p + ra, (1-r)q+ rb)`

`(1,6) to (-3(4)+4(1), -3(3) + 4(6)) = (-8,15)`

`(c,d) to ((1-r)p + rc, (1-r)q+ rd)`

`(6,7) to ( -3(4) + 4(6), -3(3) + 4(7)) = (12, 19)`

new length `l = r \sqrt{ (a-c)^2 + (b-d)^2 }`

`l = 4 \sqrt{(6-1)^2 + (7-6)^2} = 4 sqrt{26}`