A line segment has an endpoint at (-2,6) and it's midpoint is at (4,5). What is the order pair for the other endpoint of the line segment?

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03-02-2018
Mathematics

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A line segment has an endpoint at (-2,6) and it's midpoint is at (4,5). What is the order pair for the other endpoint of the line segment?

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jdoe0001 jdoe0001 · Answer 1 · 2018-02-03T00:20:47+01:00

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -2 &,& 6~) % (c,d) &&(~ x &,& y~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-2}{2}~~,~~\cfrac{y+6}{2} \right)=\stackrel{midpoint}{(4~~,~~5)}\implies \begin{cases} \cfrac{x-2}{2}=4\\\\ x-2=8\\ \boxed{x=10}\\ ------\\ \cfrac{y+6}{2}=5\\\\ y+6=10\\ \boxed{y=4} \end{cases}[/tex]