How do you find the coordinates of the other endpoint of a segment with the given Endpoint: (1,5) midpoint: (1,-6)?

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Answer 1 · 2016-05-20T14:00:53

Start point #" "->P_s->(x_s,y_s)" "->" "(1,-17)#

The distance from mid to end is the same distance from start to mid
as mid point is the mean point

Let end point be #P_e#

Let mean point be #P_m#

Let start point be #P_s#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mid to end #-> P_e-P_m#

Start to mid #-> P_m-P_s #

#color(green)("As distance from mid to each end is the same")#

we have #P_m-P_s= P_e-P_m#.......(1)

Multiply equation (1) by (-1) so that #P_s# is positive

#-P_m+P_s = +P_m - P_e#

Add #P_m# to both sides

#P_s=P_m+P_m-P_e#

#P_s=2P_m-P_e#

#P_s->(x_s,y_s)#

#x_s=2(x_m)-x_e" "->" "2(1)-1=1#

#y_s=2(y_m)-y_e" "->" "2(-6)-5=-17#

#P_s->(x_s,y_s)" "->" "(1,-17)#