Find the ratio in which the line segment joining $(2,-3)$ and $(5,6)$ is divided by $x$-axis.\

Question

Professor PC Thomas Classes · Answer

(a) : Let the point $P(x, 0)$ divides the line segment joining point $A(2,-3)$ and $B(5,6)$ in the ratio line $k: 1$.\ Coordinates of $P$ are $\left(\frac{5 k+2}{k+1}, \frac{6 k-3}{k+1}ight)$ [By section formula]\ $	herefore \quad \frac{6 k-3}{k+1}=0 \Rightarrow 6 k-3=0 \Rightarrow k=\frac{1}{2}$\ $	herefore \quad$ Point $P(x, 0)$ divides the line segment in the ratio 1: 2 .\