Alg6.13

Find the point which divides the line segment joining (-1,2) and (4,-5) in the ratio 3:2

The formula for a point which divides the line joining A(x1,y1) and (x2,y2) in the ratio l:m is

$\left(\frac{lx_2+mx_1}{l+m},\frac{ly_2+my_1}{l+m}\right)\,$

Applying the formula,

The point is

$\left(\frac{3\cdot4+2\cdot(-1)}{3+2},\frac{(3\cdot(-5)+2\cdot2}{3+2}\right)\,$

$\left(\frac{10}{5},\frac{-11}{5}\right)\,$

Hence the point is (2,-11/5)