check the picture below
thus then
[tex]\bf \qquad \textit{internal division of a line segment}\\\\
R(-2,4)\qquad S(18,-6)\qquad
ratio1=3\qquad ratio2=7\qquad 3:7\\ \quad \\ \quad \\
\cfrac{RQ}{QS}=\cfrac{ratio1}{ratio2}\implies \cfrac{R}{S}=\cfrac{3}{7}
\implies 7R=3S
\\\\\\
7(-2,4)=3(18,-6)[/tex]
[tex]\bf {{ Q=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}\\ \quad \\
\qquad thus\qquad \\ \quad \\
Q=\left(\cfrac{(7\cdot -2)+(3\cdot 18)}{3+7}\quad ,\quad \cfrac{(7\cdot 4)+(3\cdot -6)}{3+7}\right)[/tex]
