One Endpoint is 9,18 and the midpoint is 14,16 what the other end point

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15-09-2017
Mathematics

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One Endpoint is 9,18 and the midpoint is 14,16 what the other end point

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jdoe0001 jdoe0001 · Answer 1 · 2017-09-15T23:21:01+02:00

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 9}}\quad ,&{{ 18}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)[/tex]

[tex]\bf \left( \cfrac{x+9}{2}~,~\cfrac{y+18}{2} \right)=\stackrel{\textit{midpoint}}{(14,16)}\implies \begin{cases} \cfrac{x+9}{2}=14\\\\ x+9=28\\ \boxed{x=19}\\ -------\\ \cfrac{y+18}{2}=16\\\\ y+18=32\\ \boxed{y=14} \end{cases}[/tex]