1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Coordinates of Point P

  1. Sep 1, 2007 #1
    1. The problem statement, all variables and given/known data
    In the coordinate plane, the points F(-2, 1), G(1, 4), and H(4, 1) lie on a circle with center P. What are the coordinate of point P?

    2. Relevant equations

    3. The attempt at a solution

    I tried subtracting the x-values, but my answer would be always wrong. I think I'm approaching the question incorrectly.
  2. jcsd
  3. Sep 1, 2007 #2


    User Avatar
    Homework Helper

    General equation of a circle is [tex]x^2+y^2+2fx+2gy+c=0[/tex] where [tex](-f,-g)[/tex] is the centre of the circle(i.e. P) and radius,[tex]r= \sqrt{f^2+g^2-c}[/tex]

    sub the points F,G and H into this equation
    and you'll get 3 equations with 3 unknowns

    more precisely you should get to solve these equations

    Last edited: Sep 1, 2007
  4. Sep 1, 2007 #3


    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    The three points F, G, H, form a triangle; and the segment bisectors of each side will intersect at the center of the circle which contains F, G, and H. Find the lines for the segment bisectors (you only need two of them) and find their point of intersection. That is the center point of the circle.

    How do you find each line? It contains the midpoint of a side and has slope which is negative reciprocal of the side; substitute into formula for equation of a line.
  5. Sep 4, 2007 #4
    Another way is, let the coordinates of point p be (x,y). Find the point of intersection of the lines PF and GH, and let it be M. Then you can use the property PM*FM=GM*HM to solve for x and y.
  6. Sep 5, 2007 #5
    This will be the circumcentre right??? Then we can find the equations of any 2 perpendicular side bisectors and equate them.

    Am i right?
  7. Sep 5, 2007 #6


    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    Messages #3 and #5 express the same concept. Message #2 is nice because it immediately puts the information into simultaneous equations which are fairly easy to solve.

    About #3 and #5:
    The perpendicular bisectors of the sides of a triangle are concurrent (meaning they intersect) at a point equidistant from the vertices. This also means that the vertices lie on a circle whose center is that point of concurrency.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Coordinates of Point P
  1. Terminal arm Point P (Replies: 2)