Question

The coordinate of point which divides the line segment joining points $A(0,0)$ and $B(9,12)$ in the ratio $1:2$, are

• A. $(-3,4)$
• B. $(3,4)$
• C. $(3,-4)$
• D. $noneofthese$

Answer 1

The correct option is B $(3,4)$

Using the section formula, if a point $(x,y)$ divides the
line joining the points $A(x_1,y_1)$ and $B(x_2,y_2)$ 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 required point be $C(x,y)$ 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 $C$ using section formula

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

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

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

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