Determine the ratio in which the point P (m, 6)


Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.


The co-ordinates of a point which divided two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ internally in the ratio $m: n$ is given by the formula,

$(x, y)=\left(\left(\frac{m x_{2}+n x_{1}}{m+n}\right),\left(\frac{m y_{2}+n y_{1}}{m+n}\right)\right)$

Here we are given that the point P(m,6) divides the line joining the points A(−4,3) and B(2,8) in some ratio.

Let us substitute these values in the earlier mentioned formula.

$(m, 6)=\left(\left(\frac{m(2)+n(-4)}{m+n}\right),\left(\frac{m(8)+n(3)}{m+n}\right)\right)$

Equating the individual components we have


$6 m+6 n=8 m+3 n$

$2 m=3 n$


We see that the ratio in which the given point divides the line segment is.

Let us now use this ratio to find out the value of ‘m’.

$(m, 6)=\left(\left(\frac{m(2)+n(-4)}{m+n}\right),\left(\frac{m(8)+n(3)}{m+n}\right)\right)$

$(m, 6)=\left(\left(\frac{3(2)+2(-4)}{3+2}\right),\left(\frac{3(8)+2(3)}{3+2}\right)\right)$

Equating the individual components we have



Thus the value of ' $m$ ' is $-\frac{2}{5}$.

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now