How to Find the Ratio of a Line Segment
This calculator determines the ratio $m:n$ in which a point $P$ divides the line segment connecting two points $A$ and $B$.
Section Formula for Ratio
If point $P(x, y)$ divides the segment $AB$ with endpoints $A(x_1, y_1)$ and $B(x_2, y_2)$ in the ratio $k:1$ (where $k = m/n$), then:
If $k$ is positive, point $P$ divides the line internally. If $k$ is negative, it divides externally.
Example Calculation
Question: In what ratio does point P(2, 3) divide the line segment joining A(0, 1) and B(4, 5)?
Step 1: Identify coordinates.
$A(x_1, y_1) = (0, 1)$
$B(x_2, y_2) = (4, 5)$
$P(x, y) = (2, 3)$
Step 2: Use the x-coordinate formula.
$$ k = \frac{2 - 0}{4 - 2} = \frac{2}{2} = 1 $$
Step 3: Verify with y-coordinate.
$$ k = \frac{3 - 1}{5 - 3} = \frac{2}{2} = 1 $$
Answer: The ratio is 1:1 (Point P is the midpoint).
Frequently Asked Questions
What if the ratio is negative?
A negative ratio indicates external division. This means point P lies on the same line defined by A and B, but implies it is outside the segment between A and B.
Does the order of A and B matter?
Yes. The ratio $m:n$ is from A to B. If you swap A and B, the ratio becomes $n:m$.