SOLUTION: Given AB, with endpoint A at (3, -6). The midpoint M is located at (1, 2). What are the coordinates of endpoint B?

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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