How do you find the coordinates of the other endpoint of a segment with the given N(5,-09), and midpoint M(8, -7.5)?

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Answer 1 · 2017-08-12T14:42:53

#(11, - 14.1)#

First, let's find the difference between the coordinates of #M# and #N#:

#Rightarrow M - N = (8, - 7.5) - (5, - 0.9)#

#Rightarrow M - N = (8 - 5, - 7.5 - (- 0.9))#

#therefore M - N = (3, - 6.6)#

If we add this difference to #M#, we will find the coordinates of the other endpoint #O# of this segment:

#Rightarrow O = M + (M - N)#

#Rightarrow O = (8, - 7.5) + (3, - 6.6)#

#Rightarrow O = (8 + 3, - 7.5 + (- 6.6))#

#therefore O = (11, - 14.1)#

Therefore, the coordinates of the other endpoint of the segment are #(11, - 14.1)#.