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Question 1184921: Given AB, with endpoint A at (3, -6). The midpoint M is located at (1, 2). What are the coordinates of endpoint B?
Answer by greenestamps(13206)   (Show Source):
You can put this solution on YOUR website!
Here first is a formal mathematical solution....
The x coordinate of the midpoint is the average of the x coordinates of the endpoints; the y coordinate of the midpoint is the average of the y coordinates of the endpoints:
The midpoint between A(3,-6) and B(p,q) is M((3+p)/2,((-6+q)/2).
The midpoint is M(1,2). So...
x coordinates:
(3+p)/2=1
3+p=2
p=-1
y coordinates:
(-6+q)/2=2
-6+q=4
q=10
ANSWER: The coordinates of B are (p,q)=(-1,10)
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But you don't learn much by plugging numbers into formulas; you will understand the problem a lot better if you solve it informally.
Imagine you are walking in a straight line from A(3,-6) towards B, and you are halfway there when you reach (1,2).
At the midpoint (1,2) you have moved -2 units in the x direction -- from 3 to 1. So to get to the end you need to move another -2 units in the x direction from 1.
1-2=-1; the x coordinate of B is -1.
At the midpoint (1,2) you have moved 8 units in the y direction -- from -6 to 2. So to get to the end you need to move another 8 units in the y direction from 2.
2+8=10; the y coordinate of B is 10.
ANSWER: B(-1,10)
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