Question 1145847: The midpoint of (UV) ̅ is (6, 7). The coordinates of one endpoint are U(3, -5). Find the coordinates of endpoint V.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
The midpoint of ( ) ̅ is ( ,  ).
( , ) = (, )
The coordinates of one endpoint are U( ,  ).
( , ) = (, )
the coordinates of endpoint V are ( , )
sketch looks like this:
 -------------------------------------------- --------------------------------------------
or
(,) --------------------------------(,) ---------------------------------------(,)
we know that
(, )----------------------------------- (, )-----------------------------------(,)
as you know the midpoint of () coordinates are
(, )=(,)=( ,( )
since  ,  ,  ,  , we have:
 => => => =>
 => => => => =>
so, the coordinates of endpoint are (,)=( , )
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
We know that to get from the midpoint (6,7) to endpoint U(3,-5) we need to go 3-6 = -3 in the x direction and -5-7 = -12 in the y direction.
So to get from the midpoint to the other endpoint we need to go +3 in the x direction and +12 in the y direction:
V = (6+3,7+12) = (9,19)
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