Question

The ratio in which the line joining of (-2,5) and (1,-9) is divided by the x-axis is

• A. $5:9$
• B. $2:1$
• C. $4:5$
• D. $4:9$

Answer 1

Answer: (A)

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

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

Let the ratio AP:PB be k:1

Therefore, y-coordinate of $P=\frac{\left(k\right)(-9)+\left(1\right)\left(5\right)}{k+1}$
or -9k + 5 = 0
or $k=\frac{5}{9}$
$\therefore$ Ratio = 5:9