Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 9) internally in the ratio 2 : 3.
Answer Details
To solve this problem, we will use the section formula.
Let the point which divides the line segment PQ internally in the ratio 2:3 be R(x,y). Then we have:
\begin{align*}
x = \frac{3\times(-2) + 2\times4}{2+3} = \frac{6}{5} \\
y = \frac{3\times3 + 2\times9}{2+3} = \frac{24}{5}
\end{align*}
Therefore, the coordinates of R are \((\frac{6}{5},\frac{24}{5})\), which corresponds to option (B).