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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asked Feb 26, 2019 38.8k views

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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?

Mathematics
college

LenB asked

by LenB

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1 Answer

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

KR Akhil answered Mar 3, 2019