Alg6.15

Find the ratio in which the point P(2,1)divide the line segment joining the points A(1,-2) and B(4,7).

Let the ratio be a:1

Hence the point of dividing is

$\left(\frac{4a+7}{a+1},\frac{7a-2}{a+1}\right)=(2,1)\,$

Now comparing both sides,we get

$\frac{4a+1}{a+1}=2,\frac{7a-2}{a+1}=1\,$

$4a+1=2a+2,7a-2=a+1\,$

$a=\frac{1}{2},a=\frac{1}{2}\,$

Hence the ratio is 1:2