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One endpoint of a line segment is at (4, 2). The line is bisected by placing the midpoint of the line segment at (−2, −1). What are the coordinates of the other endpoint? A) (−4, −6) B)(−8, −4) C)(10,
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One endpoint of a line segment is at (4, 2). The line is bisected by placing the midpoint of the line segment at (−2, −1). What are the coordinates of the other endpoint?

A) (−4, −6)
B)(−8, −4)
C)(10, 5)
D)(−8, 4)

User Bbholzbb
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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) &&(~ 4 &,& 2~) % (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+4}{2}~~,~~\cfrac{y+2}{2} \right)=\stackrel{midpoint}{(-2~~,~~-1)}\implies \begin{cases} \cfrac{x+4}{2}=-2\\\\ x+4=-4\\ \boxed{x=-8}\\ ----------\\ \cfrac{y+2}{2}=-1\\\\ y+2=-2\\ \boxed{y=-4} \end{cases}
User Unclemeat
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