check the picture below
for point C
\bf \textit{internal division of a line segment} \\ \quad \\\\A(1,4)\qquad B(6,-1)\qquad ratio1=2\qquad ratio2=3\qquad 2:3 \\\\\\ \cfrac{A{ C }}{{ C }B}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot A=ratio1\cdot B\quad \implies 3(1,4)=2(6,-1) \\ \quad \\\\{{ C=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}\\ \quad \\
\bf thus\\\\\\C=\left(\cfrac{(3\cdot 1)+(2\cdot 6)}{2+3}\quad ,\quad \cfrac{(3\cdot 4)+(2\cdot -1)}{2+3}\right)
and for point D
\bf \textit{internal division of a line segment} \\ \quad \\\\ A(1,4)\qquad B(6,-1)\qquad ratio1=3\qquad ratio2=2\qquad 3:2 \\\\\\ \cfrac{A{ D }}{{ D }B}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot A=ratio1\cdot B\quad \implies 2(1,4)=3(6,-1) \\ \quad \\\\ {{ D=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}
\bf thus \\\\\\ D=\left(\cfrac{(2\cdot 1)+(3\cdot 6)}{3+2}\quad ,\quad \cfrac{(2\cdot 4)+(3\cdot -1)}{3+2}\right)
