SOLUTION: The midpoint of (UV) ̅ is (6, 7). The coordinates of one endpoint are U(3, -5). Find the coordinates of endpoint V.

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(13203) (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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