A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

If the vertices of triangle ABC are A(2, -1), B(0, 2) and C(4, -3), what are the coordinates of the circumcenter?

  • This Question is Closed
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Draw it :)

  2. mathmate
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It is a very obtuse triangle. The three points lie almost on a straight line. Back to basics, a circumcentre is a point which is equidistant to all three points, so that it is the centre of a circle that passes through all three points. Using Pythagoras theorem, and assuming the required circumcentre is at (x0,y0), then R=radius of circumcircle and R^2=(Xa-X0)^2+(Ya-Y0)^2=(Xb-X0)^2+(Yb-y0)^2=(Xc-x0)^2+(Yc-y0)^2 You will have a system of two linear equations (since all the x0^2 and y0^2 terms cancel out) from which you can solve for X0 and Y0. (Xa-X0)^2+(Ya-Y0)^2=(Xb-X0)^2+(Yb-y0)^2 reduces to 6y-4x+1=0 and (Xb-X0)^2+(Yb-y0)^2=(Xc-x0)^2+(Yc-y0)^2 reduces to -10y+8x-21=0 from which you can solve for X0 and Y0. Hint: X0+Y0=24 (for checking purpo|dw:1327108062011:dw|ses).

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.