Question

To find a point $P$ on the line segment $AB=6cm$, such that $AP:AB=2:5$, in which ratio does the line segment $AB$ is divided by $P$?

Answer 1

Given that

$AB=6cm,$ $\frac{AP}{AB}=\frac{2}{5}$

$AB=6cm$ __ (1)

$\frac{AP}{AB}=\frac{2}{5}$

$AP=\frac{2}{5}\times AB$

$=\frac{2}{5}\times 6$

$AP=\frac{12}{5}$

$AP=2.4cm$__ (2)

$AP+PB=AB$

$2.4+PB=6$

$PB=6-2.4$

$PB=3.6cm$ __ (3)

Ratio = $\frac{AP}{PB}=\frac{2.4}{3.6}$

$=\frac{24}{10}\times \frac{10}{36}$

$=\frac{24}{36}$

$=\frac{2}{3}$

$\therefore$ The Ratio is $2:3$