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Q: Hello! I have a question with circles I'm finding difficult. "In circle O, diameter RS has endpoints R(3a,2b-1) and S(a-6,4b+5). Find the coordinates of point O, in terms of a and b. Express your answer in simplest form."

Hello Meagan, i will be happy to offer assistance.

Since the circle is O, O is the center. If you know the endpoints of the diameter, then use the midpoint formula to find the coordinates of the center.

Midpoint Formula

( (x1 + x2)/2, (y1 + y2)/2)

Basically, take the average of the x ordinates and the average of the y ordinates.

Plugging the values in gets

((3a + a - 6)/2, (2b - 1 + 4b + 5)/2)

((4a - 6)/2, (6b + 4)/2)

(2a - 3, 3b + 2)

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