Question

If the line segment joining the points $A(3,4)$ and $B(14,-3)$ meets the x-axis at $P$, then the ratio in which $P$ divides the segment $AB$ is

• A. $4:3$
• B. $3:4$
• C. $2:3$
• D. $4:1$

Answer 1

The correct option is A $4:3$

Given $A(3,4),B(14,-3)$

Let $m:n$ be the ratio in which point $P$ divides line segment $AB$ and let $(x,y)$ be the coordinates of the point $P$.

Since, $P$ is the point of intersection of line $AB$ with the $x-axis$, the $y-coordinate$ of $P$ equals $0$.

Then, the coordinates of $P$ is $(x,0)$

now, using section formula for $y-coordinate$ of point $P$ we have,

$y=\frac{m\times (-3)+n\times 4}{m+n}$

$0=\frac{-3m+4n}{m+n}$

$-3m+4n=0$

$3m=4n$

$\frac{m}{n}=\frac{4}{3}$

Therefore, the required ratio is $4:3$.