Mathematics, 23.06.2019 11:30 mktdonaldson
Find the coordinates of point z that splits the segment xy located 3/7 of the way between x(-2,1) and y(4,5).
Answers: 2
then 
![\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ X(-2,1)\qquad Y(4,5)\qquad \qquad \stackrel{\textit{ratio from X to Y}}{3:4} \\\\\\ \cfrac{X\underline{Z}}{\underline{Z} Y} = \cfrac{3}{4}\implies \cfrac{X}{Y} = \cfrac{3}{4}\implies 4X=3Y\implies 4(-2,1)=3(4,5)\\\\[-0.35em] ~\dotfill\\\\ Z=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill](/tpl/images/1201/0152/5adc1.png)
![\bf Z=\left(\cfrac{(4\cdot -2)+(3\cdot 4)}{3+4}\quad ,\quad \cfrac{(4\cdot 1)+(3\cdot 5)}{3+4}\right)\implies Z=\left(\cfrac{-8+12}{7}~,~\cfrac{4+15}{7} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( \cfrac{4}{7}~~,~~\cfrac{19}{7} \right)~\hfill](/tpl/images/1201/0152/e9c0c.png)
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Find the coordinates of point z that splits the segment xy located 3/7 of the way between x(-2,1) an...
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