Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​( -4−10​), endpoint ​(2.−13​)

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Question:

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)
midpoint ​( -4−10​), endpoint ​(2.−13​)

Answers

Answer:The required points of the given line segment  are ( - 10, - 7 ).Step-by-step explanation:Given that the line segment AB whose midpoint M is ( - 4, -10 ) and point A is ( 2, - 13), then we have to find point B of the line segment AB -As we know that-If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex] )then the mid points M are- M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex]  )Here,Let A ( 2, - 13 ), B ( x, y ) with midpoint M ( - 4, - 10 ) -then by the midpoint formula M are-( - 4, - 10 )  = ( [tex]\frac{ 2 + x}{2}[/tex] , [tex]\frac{- 13 + y}{2}[/tex] )On comparing x coordinate and y coordinate -We get,( [tex]\frac{x + 2}{2}[/tex] = - 4  ,  [tex]\frac{ - 13 + y}{2}[/tex] = - 10)( x + 2 = - 8, - 13 + y = - 20 )( x = - 8 - 2, y = - 20 + 13 )( x = - 10, y = - 7 )Hence the required points  A are ( - 10, - 7 ).We can also verify by putting these points into Midpoint formula.

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