Question

In what ratio, does $P(4,6)$ divide the join of $A(-2,3)$ and $B(6,7)$

Answer 1

Given that:

$A(-2,3)$ and $B(6,7)$ are the end-points and point $P(4,6)$ divide the line.

To find:

$\frac{m}{n}=?$

Solution:

Let point $P(4,6)$ divide the line internally in the ratio $m:n.$

$x$-coordinate of $P$$:4=\frac{6m+(-2n)}{m+n}$

or, $4\times (m+n)=6m-2n$

or, $4m+4n=6m-2n$

or, $2m=6n$

or, $\frac{m}{n}=\frac{3}{1}$

So, point $P(4,6)$ divide the line in the ratio $3:1.$