brisaperez brisaperez
  • 25-03-2018
  • Mathematics
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The midpoint of ST has coordinates (5,-8). Find the coordinate of point S when T (10,18)

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jdoe0001 jdoe0001
  • 25-03-2018
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &S&(~ x&,& y~) % (c,d) &T&(~ 10 &,& 18~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{10+x}{2}~,~\cfrac{18+y}{2} \right)~~=~~\stackrel{midpoint}{(5,-8)}\implies \begin{cases} \cfrac{10+x}{2}=5\\\\ 10+x=10\\ \boxed{x=0}\\ -------\\ \cfrac{18+y}{2}=-8\\\\ 18+y=-16\\ \boxed{y=-34} \end{cases}[/tex]
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