Ponto que Divide Segmento (razão)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
divisão em razão k
About this calculator
This calculator determines the coordinates of point P that divides a line segment AB in a given ratio k. The formula used is P = ((x1 + k*x2)/(1 + k), (y1 + k*y2)/(1 + k)), where (x1, y1) and (x2, y2) are the endpoints. The parameter k indicates the ratio of distances AP to PB: if k > 0, P lies between A and B; if k = 0, P coincides with A; if k < 0, P is outside the segment (external division).
To use the tool, enter the coordinates of points A and B and the value of k. The result gives point P that divides the segment in the specified ratio. It is useful in analytic geometry problems, such as finding points on lines or calculating coordinates of points that divide a segment proportionally.
Use cases include: dividing a segment into equal parts (k = 1), finding the midpoint (k = 1), or locating a point at a specific distance from an endpoint. It is also applicable in engineering, architecture, and computer graphics for linear interpolation.
Caution: ensure that k ≠ -1, as this results in division by zero. For negative k, point P lies outside the segment, which may be unintended if internal division is desired. Always check the sign of k according to the problem context.
Frequently asked questions
What does the ratio k mean?
The ratio k is the relationship between distances AP and PB, i.e., AP / PB = k. If k is positive, point P lies between A and B; if k is negative, P is outside the segment.
Can I use k = 0?
Yes, when k = 0, point P coincides with point A, since the distance AP is zero.
What happens if k = -1?
If k = -1, the formula results in division by zero (1 + k = 0), so it cannot be computed. This occurs because the point would be at infinity.
How do I find the midpoint using this calculator?
For the midpoint, use k = 1. The formula reduces to P = ((x1+x2)/2, (y1+y2)/2).
Does this calculator work for external division?
Yes, for external division use a negative k. For example, k = -2 indicates that P is outside the segment, with AP = 2 * PB but in the opposite direction.