Question

find the point that divides the line - segment joining (-2,3) and (4,9) in the ratio 2:1.

Explanation:

Step1: Recall the section - formula

The formula to find the point $(x,y)$ that divides the line - segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $(x_1,y_1)=(-2,3)$, $(x_2,y_2)=(4,9)$, $m = 2$, and $n = 1$.

Step2: Calculate the x - coordinate

$x=\frac{2\times4+1\times(-2)}{2 + 1}=\frac{8-2}{3}=\frac{6}{3}=2$.

Step3: Calculate the y - coordinate

$y=\frac{2\times9+1\times3}{2 + 1}=\frac{18 + 3}{3}=\frac{21}{3}=7$.

Answer:

The point is $(2,7)$