Question
calculate point P on AB such that the ration of AP to PB is 1:3
Answers
GPT-5 mini
To find the point P on segment AB with AP:PB = 1:3 (internal division), P is one-quarter of the way from A to B.
If A = (x1, y1) and B = (x2, y2), then
- vector form: P = A + (1/4)(B − A)
- coordinate form: P = ((3x1 + x2)/4, (3y1 + y2)/4)
(Works the same in 3D: P = ((3x1 + x2)/4, (3y1 + y2)/4, (3z1 + z2)/4).)
Example: A = (0,0), B = (4,0) → P = (1,0).
If you meant an external division or have specific coordinates, tell me and I’ll compute it.
If A = (x1, y1) and B = (x2, y2), then
- vector form: P = A + (1/4)(B − A)
- coordinate form: P = ((3x1 + x2)/4, (3y1 + y2)/4)
(Works the same in 3D: P = ((3x1 + x2)/4, (3y1 + y2)/4, (3z1 + z2)/4).)
Example: A = (0,0), B = (4,0) → P = (1,0).
If you meant an external division or have specific coordinates, tell me and I’ll compute it.