Question

Find the coordinates of a point P on th eline segment joining A(1,2) and B(6,7) such that AP=$\frac{2}{5}AB.$

Answer 1

Given,A(1,2) and B(6,7) are the given point of a line segment AB with a point P on it.

Let the co-ordinate of point P be (x,y)

$AP=\frac{2}{5}AB$ (Given)


AB=AP+PB
$\Rightarrow \frac{AP}{PB}=\frac{2}{3}$

$\therefore$ m=2,n=3

Then, bysection formula, we have

$x=\frac{m{x}_2+n{x}_1}{m+n}andy=\frac{m{y}_2+n{y}_1}{m+n}$

$x=\frac{2\times 6+3\times 1}{2+3}andy=\frac{2\times 7+3\times 2}{2+3}$

$x=\frac{15}{5}andy=\frac{20}{5}$

x=3 and y=4