Question 214019
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)
 
C(-4,-5)

M(3,-6)


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,


{{{3=(x+(-4))/2}}} and  {{{-6=(y+(-5))/2}}}


{{{6=x-4}}} and {{{-12=y-5}}}


{{{x=10}}} and {{{y=-7}}}


So the other endpoint is (10,-7)


As a check between the two endpoints (10,-7) and (-4,-5), let's calculate the midpoint.


{{{(10+(-4))/2=3}}} is the x-coordinate for the midpoint.


{{{(-7+(-5))/2=-6}}} is the y-coordinate for the midpoint.


So the midpoint is (3,-6) which is same as before.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J