Find the coordinates of the point that divides the line segment connecting $\mathrm{A}(0,0)$ and $B(9,12)$in the ratio 1 : 2.

Using the section formula, if a point (x, y) divides the line joining the points $\mathrm{A}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ and $\mathrm{B}\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)$ in the ratio $\mathrm{m}:\mathrm{n}$, then

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

Let the required point be $\mathrm{C}(\mathrm{x},\mathrm{y})$ which divides the line segment joining points A(0,0) and B(9,12) in ratio 1:2

$m_1=1,m_2=2$

Then we can calculate the coordinates of $\mathrm{C}$ using section formula

$(x,y)=\left[\frac{m_1\times x_2+m_2\times x_1}{m_1+m_2},\frac{m_1\times y_2+m_2\times y_1}{m_1+m_2}\right]$

$(\mathrm{x},\mathrm{y})=\left[\frac{1\times 9+2\times 0}{1+2},\frac{1\times 12+2\times 0}{1+2}\right]$

$(x, y)=(3,4)$

Hence, coordinates of C will be (3,4).