SOLUTION: If AB is the diameter of a circle with centre O (4,5) and A (8,3), find B.

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Question 1109038: If AB is the diameter of a circle with centre O (4,5) and A (8,3), find B.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Point B is some (x,y) ordered pair, and O(4,5) is the midpoint of A(8,3) and the point B(x,y). Use the MidPoint Formula.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Using the midpoint formula, as the other tutor suggested, is fine. But plugging numbers into formulas usually doesn't teach you anything; it is perhaps more beneficial to you to solve the problem using a bit of logical reasoning.

You know where the center of the circle is, at (4,5). And you know one end point of a diameter is (8,3).

To get from the center to the known end of a diameter, you move 4 units to the right (from 4 to 8) and 2 units down (from 5 to 3).

So to get to the other end of that same diameter, from the center you need to do exactly the opposite: go 4 units to the left (from 4 to 0) and 2 units up (from 5 to 7).

Answer: B is (0,7).