Name: Jessica Sipes
Who is asking: Student
Level: Middle
Question:
I need to know how to find and endpoint using the midpoint and the other endpoint.
Hi Jessica,
Since you didn't ask about finding the midpoint if you know the endpoints I assume that you can do that. That is if the endpoints of a line are (x_{1},y_{1}) and (x_{2},y_{2}) then the coordinates of the midpoint are (x_{1}+x_{2})/2 and (y_{1}+y_{2})/2. This is easy to remember because the xcoordinate of the midpoint is half way between the xcoordinates of the endpoints and the ycoordinate of the midpoint is half way between the ycoordinates of the endpoints.
You can use this same expression to find an endpoint if you know the other endpoint and the midpoint. Let me explain with an example.
Suppose that (2,4) is an endpoint and (5,6) is the midpoint. Let (2,4) be (x_{1},y_{1}) then
5 = (x_{1} + x_{2})/2 = (2 + x_{2})/2
Multiply both sides by 2 to get 2(5) = 2 + x_{2}
and thus x_{2} = 10  2 = 8
In a similar fashion
6 = (y_{1} + y_{2})/2 = (4 + y_{2})/2
Multiply both sides by 2 to get 2(6) = 4 + y_{2}
and thus y_{2} = 12 + 4 = 16.
Cheers,
Penny
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