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A point $P$ divides the line segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ internally in the ratio $m_1:m_2$, where $PA:PB=m_1:m_2$. Which are the coordinates of $P$? 
A$\left(\dfrac{m_1x_1+m_2x_2}{m_1+m_2},\dfrac{m_1y_1+m_2y_2}{m_1+m_2}\right)$
B$\left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$
C$\left(\dfrac{x_1+x_2}{m_1+m_2},\dfrac{y_1+y_2}{m_1+m_2}\right)$
D$\left(\dfrac{m_1x_2-m_2x_1}{m_1+m_2},\dfrac{m_1y_2-m_2y_1}{m_1+m_2}\right)$
Answer & Solution
Correct answer: B. $\left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$
The section formula for internal division is $\left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$. The weights are attached opposite to the endpoints because the ratio is $PA:PB=m_1:m_2$.
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