Question

The ratio in which the line segment joining (3, 4) and (-2, -1) is divided by the x-axis is:

• A. 3 : 2
• B. 4 : 1
• C. 4 : 3
• D. None of these

Answer 1

Answer: (B)

4 : 1

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 $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Substituting $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(-2,-1)$ in the section formula, we get the point $(\frac{m(-2)+n\left(3\right)}{m+n},\frac{m(-1)+n\left(4\right)}{m+n})=(\frac{-2m+3n}{m+n},\frac{-m+4n}{m+n})$

As the point lies on x - axis, we have the y -coordinate $=0$.
$=>\frac{-m+4n}{m+n}=0$
$=>m=4n$ or $m:n=4:1$