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Math Help - Points on a circle.

  1. #1
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    Points on a circle.

    Guys, i have one question in math.
    here it it.
    The diameter of a circle has the endpoints (9,5) and (3,-8). Find the center of the circle and at least two other points on the circle.
    thank you!
    Last edited by mr fantastic; December 14th 2010 at 06:38 PM. Reason: Re-titled.
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  2. #2
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    Well since we know the diameter's endpoints the centre of the circle must be the midpoint of the 2 points.

    We can use the midpoint formula:

    \displaystyle (\frac {x_{1}+x_{2}}{2} , \frac {y_{1}+y_{2}}{2})

    Sub in the values to find the midpoint
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  3. #3
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    yes. i did that and found the midpoint of (6,-1.5)
    but doesn't it says that i have to find other two points on the circle?
    i'm so confused.
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  4. #4
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    Now you know the centre,you can find the radius: r = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} but in this case (x_1,y_1) is the centre and (x_2,y_2) is either point.

    Once you know the radius use the equation of a circle to pick any old points: (x-a)^2 + (y-b)^2 = r^2 with centre (a,b) and radius r
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  5. #5
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    my teacher didn't taught us anything about the square rot and that big "E" thing.
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  6. #6
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    lol the big E thing is his sig, it has nothing to do with his post

    HAHAHAHAHAH xD
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  7. #7
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    The big E thing is in the poster's signature, it is not part of the response!

    You have been shown how to find the centre in post #2 and from this apply the radius from post #4 to this centre point, here's two easy solutions, given (x,y) is the centre and r your radius then you have (x+r,y) and (x,y+r)
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  8. #8
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    points on a circle

    the slope diagramof the given diameter points is 13/6. Its radius slope diagram is 6.5/3.
    A diameter perpendicular to the given diameter has a slope of -6/13 and its radius slope diagram is -3/6.5.
    Working with these new radius slopes and starting at the circle center the end points on the circle are determined to be (-.5,1.5) and (12.5,-4.5) by moving 6.5 points right and left of center and 3 points up and down of center



    bjh
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  9. #9
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    Do you know the formula for distance between two points?

    The distance from (x_1, y_1) to (x_2, y_2) is \sqrt{(x_1- x_2)^2+ (y_1-y_2)^2}.

    You can use that to find the distance form (6, 1.5), the center of the circle, to either (9, 5) or (3, -8), the radius of the circle, then find values of (x, y) such that the distance from (x, y) to (6, -1.5) is that radius. (There will be an infinite number of such points, of course. Choose some convenient value for x and determine y satifying that equation.)
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