Question

A line segment has endpoints at `(9 ,2 )` and `(7 , 4)`. The line segment is dilated by a factor of `3` around `(1 , 5)`. What are the new endpoints and length of the line segment?

Answer 1

`(9,2) to (25, -4)`

`(7,4) to (19,2)`

New length `6 sqrt{2}`

Explanation:

There is indeed a Bolivia, United States, in North Carolina, not too far from Myrtle Beach.

I did the general case of this question [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)

I got for endpoints `(a,b),(c,d),` and factor `r` around dilation point `(p,q):`

`(a,b) to ( (1-r)p + ra, (1-r)q+ rb)`, similarly for `(c,d)`,

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

These are old problems that probably no one ever looks at that I think are just here to give the noobs something to do. I'm an old timer at 26 days; I only answered because of Bolivia, United States.

I will now mindlessly substitute.

`a=9,b=2,c=7,d=4,p=1,q=5,r=3`

`(9,2) to ( (1-3)1 + 3(9), (1-3)5+ 3(2))= (25, -4)`

`(7,4) to ( (1-3)1 + 3(7), (1-3)5+ 3(4)) = (19,2)`

new length `l = 3 \sqrt{ (9-7)^2 + (2-4)^2 } = 3 sqrt{8} =6 sqrt{2}`