Class 10

Math

All topics

Coordinate Geometry

Find 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.

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ in the ratio $m:n$, then

$(x,y)=(m+nmx_{2}+nx_{1} ,m+nmy_{2} +ny_{1} )$

Let P divides the join of A and B in the ratio $k:1$, then

Therefore, we have

$6=(k×8+1×3)/(k+1)$

$⇒6k+6=8k+3$

or $k=3/2$

P divides the join of A and B in the ratio $3:2$

Now, $m=(2k−4)/(k+1)=(2×3/2−4)/(3/2+1)$

$=−1/(5/2)$

$=−2/5$.