Question 214006
You are given an endpoint and the midpoint of a line segment. Find the coordinates of the other endpoint. Each midpoint is denoted by M(x, y)

 
B (5,7)
 
M (-1,0)
  

Let (x,y) be the other endpoint.  Then for this example the midpoint is calculated by averaging the x and y coordinates of the endpoints.  That is,


{{{-1=(x+5)/2}}} and  {{{0=(y+7)/2}}}


{{{-2=x+5}}} and {{{0=y+7}}}


{{{x=-7}}} and {{{y=-7}}}


So the other endpoint is (-7,-7)


As a check between the two endpoints (-7,-7) and (5,7), let's calculate the midpoint.


{{{(-7+5)/2=-1}}} is the x-coordinate for the midpoint.


{{{(-7+7)/2=0}}} is the y-coordinate for the midpoint.


So the midpoint is (-1,0) which is same as before.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J