Need some GCSE maths help

[Cheetah Designs]

EDIT:
I abstracted the question too much and now I fail at applying the logic.

I have:
- old_length
- new_length (could be any length...bigger or smaller than old_length)
- coordinates (x1, y1) & (x2, y2)
- (x1,y1) - (u1, v1) = (u2, v2) - (x2, y2)

I need to find:
- coordinates (u1, v1) & (u2, v2)



Brain isn't working:

Orange line is half the length of the blackline and centered within/ontop of it. I know (x1,y1) and (x2, y1)......how do i get (u1,v1) and (u2,v2).

Don't need an explanation just the answer. Can it be done without trig?

Thanks.

 

[Cheetah Designs]

I abstracted the question too much and now I fail at applying the logic.

I have:
- old_length
- new_length (could be any length...bigger or smaller than old_length)
- coordinates (x1, y1) & (x2, y2)
- (x1,y1) - (u1, v1) = (u2, v2) - (x2, y2)

I need to find:
- coordinates (u1, v1) & (u2, v2)