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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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Anne Losch


I cannot answer questions about non-Euclidean geometry (that has been a while). I can answer trigonometry, coordinate geometry, proofs, algebraic geometry, transformations, constructions, 3d shapes, area, perimeter, points, lines, planes, angles (adjacent, vertical, ...), parallel and perpendicular lines, polygons, circles, and anything taught in a geometry class.


I have two years teaching experience in geometry; many years tutoring Geometry.

NEA, past NCTM, MAA, AMS, and ASCD

I have a B.S. in mathematics (and computer science), and went back for my teaching certificate (with more than enough hours for a minor in education).

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Past tutoring at Sylvan Learning Center, Huntington Learning Center, and private tutor. I have responded to questions on but would prefer to volunteer with All Experts.

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