Question

If point Pis 3/8 of the distance from A to B, then point P partitions the line segment from A to B into aratio.

Answer 1

We can start by drawing the segment:

We know that AP is 3/8 of the distance AB.

We then know that:

$PB=AB-AP=AB-\frac{3}{8}AB=(1-\frac{3}{8})AB=\frac{5}{8}AB$

Then, the ratio between the two segments become:

$\frac{AP}{PB}=\frac{\frac{3}{8}AB}{\frac{5}{8}AB}=\frac{3}{8}\cdot\frac{8}{5}=\frac{3}{5}$

The ratio AP/PB is 3/5.

(If we express this as PB/AP the ratio would be 5/3).