SOLUTION: The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?

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Question 547152: The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the center of the circle is at (4,6), the diameter that has one end at (2,5) must have the other end at (6,7).
The other end must be at the same distance and on the same line.
Let's call the point we are looking for (x,y).
You could say that the center of the circle is the midpoint of that diameter and so
4=%28x%2B2%29%2F2 and 6=%28y%2B5%29%2F2 and solve those equations for x and for y
In my head, I just figured that if going from (2,5) to center (4,6) I had to add 2 to the x-coordinate and 1 to the y-coordinate, doing the same again would get me to the other end of the diameter, so I added 4%2B2=6 and 6%2B1=7 in my head. It would have worked well for speed, if there was no show-your-work rule.