Definition:Division in Ratio/Straight Line

Definition

Let $A$, $B$ and $P$ be collinear points.

Then:

$P$ divides $AB$ in the ratio $m : n$

if and only if:

$AP : PB = m : n$

where $AP$ and $PB$ are directed line segments.

Internal

Let $A$, $B$ and $P$ be collinear points.

Let $P$ lie between $A$ and $B$.

Then $P$ divides $AB$ internally in the ratio $m : n$ if and only if:

$AP : PB = m : n$

and the ratio $m : n$ is positive.

External

Let $A$, $B$ and $P$ be collinear points.

Let $P$ not lie between $A$ and $B$.

Then $P$ divides $AB$ externally in the ratio $\size m : \size n$ if and only if:

$AP : PB = m : n$

and the ratio $m : n$ is negative.

Also see

• Results about division in ratio can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): division in a given ratio: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): division in a given ratio: 2.