so hmm check the picture below, so the segment BZ is split in 6 pieces, 5 go to BH and HZ takes 1
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
B(3, -1)\qquad Z(12,5)\qquad
ratio1=5\qquad ratio2=1\qquad 5:1
\\\\\\
\cfrac{BH}{HZ} = \cfrac{5}{1}\implies \cfrac{B}{Z} = \cfrac{5}{1}\implies 1\cdot B=5\cdot Z
\\\\\\
1(3,-1)=5(12,5)\\\\
-------------------------------\\\\[/tex]
[tex]\bf { H=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}\\\\
-------------------------------\\\\
H=\left(\cfrac{(1\cdot 3)+(5\cdot 12)}{5+1}\quad ,\quad \cfrac{(1\cdot -1)+(5\cdot 5)}{5+1}\right)[/tex]
