Question

A point H on a segment with end points B(3,-1) and Z(12,5) partitions the segment in a 5:1 ratio. Find H. Show all work

Answer 1

So hmm check the picture below, so the segment BZ is split in 6 pieces, 5 go to BH and HZ takes 1

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ B(3, -1)\qquad Z(12,5)\qquad ratio1=5\qquad ratio2=1\qquad 5:1 \\\\\\ \cfrac{BH}{HZ} = \cfrac{5}{1}\implies \cfrac{B}{Z} = \cfrac{5}{1}\implies 1\cdot B=5\cdot Z \\\\\\ 1(3,-1)=5(12,5)\\\\ -------------------------------$

$\bf { H=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}\\\\ -------------------------------\\\\ H=\left(\cfrac{(1\cdot 3)+(5\cdot 12)}{5+1}\quad ,\quad \cfrac{(1\cdot -1)+(5\cdot 5)}{5+1}\right)$