Point $R$ divides $PQ$ internally in the ratio $m_1:m_2$, where $P(x_1,y_1)$ and $Q(x_2,y_2)$. The coordinates of $R$ are:

1. Internal division uses a sum in both numerator and denominator; a difference gives external division. 2. Similar triangles give $\dfrac{PR}{RQ}=\dfrac{m_1}{m_2}$, so $m_2(x-x_1)=m_1(x_2-x)$. 3. Rearranging: $x(m_1+m_2)=m_1x_2+m_2x_1$, hence $x=\dfrac{m_1x_2+m_2x_1}{m_1+m_2}$. 4. The same argument in $y$ gives $y=\dfrac{m_1y_2+m_2y_1}{m_1+m_2}$. 5. The form with minus signs throughout is the external-division formula, and the one pairing $m_1$ with $x_1$ attaches each ratio part to the wrong endpoint. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 8: Coordinate Geometry I_