Results 1 to 4 of 4

Math Help - Point equidistant to 3 or more other points

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    2

    Point equidistant to 3 or more other points

    Hi!

    Hope this is posted in the right section - if not please advise.

    If there are 2 points, (x1 y1) and (x2 y2), the equidistant point is at the midpoint at location ((x1+x2)/2) ((y1+y2)/2)

    eg if there are 2 points p and q at locations (1,2) and (3,0) the point equidistant is at (2,1) - the midpoint m

    y
    4 |
    3 |
    2 |p
    1 | m
    _ |__q_______ x
    0 1 2 3 4

    Suppose there are more than 2 points? Is there a formula for working out the point equidistant to the n points?

    eg if there are 3 points p q r at locations (1,2) (3,0) and (3,2), the point equidistant is still at (2,1), but I can't see a way of computing this from the figures.

    y
    4 |
    3 |
    2 |p--r
    1 | m
    _ |__q_______ x
    0 1 2 3 4 NB hyphens are spaces-board changes 2 spaces to 1

    This is not a test question or homework crib - I am in my late fifties and just interested in mathematics!

    The thought occured to me and I just cant see a solution for the general case Equidistant point of points (x1 y1) (x2 y2) (x3 y3) ... (xn yn)

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello RSDonovan

    Welcome to Math Help Forum!
    Quote Originally Posted by RSDonovan View Post
    Hi!

    Hope this is posted in the right section - if not please advise.

    If there are 2 points, (x1 y1) and (x2 y2), the equidistant point is at the midpoint at location ((x1+x2)/2) ((y1+y2)/2)

    eg if there are 2 points p and q at locations (1,2) and (3,0) the point equidistant is at (2,1) - the midpoint m

    y
    4 |
    3 |
    2 |p
    1 | m
    _ |__q_______ x
    0 1 2 3 4

    Suppose there are more than 2 points? Is there a formula for working out the point equidistant to the n points?

    eg if there are 3 points p q r at locations (1,2) (3,0) and (3,2), the point equidistant is still at (2,1), but I can't see a way of computing this from the figures.

    y
    4 |
    3 |
    2 |p--r
    1 | m
    _ |__q_______ x
    0 1 2 3 4 NB hyphens are spaces-board changes 2 spaces to 1

    This is not a test question or homework crib - I am in my late fifties and just interested in mathematics!

    The thought occured to me and I just cant see a solution for the general case Equidistant point of points (x1 y1) (x2 y2) (x3 y3) ... (xn yn)

    Thanks in advance!
    You're only partly correct in saying that the mid-point of the line joining two points is equidistant from the two points. This is true, but so are all the points on the perpendicular bisector of the line.

    Therefore, to find a point that is equidistant from three points, draw the perpendicular bisectors of the lines joining two pairs of these points. Their point of intersection is equidistant from all three points (provided, of course, that they are not parallel).

    This point is, of course, the centre of the circle passing through the three given points, and is always a unique point provided that the three points don't lie in a straight line. But in general, you won't be able to do this for four (or more) points, unless they happen to form a cyclic quadrilateral.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    2
    Thanks Grandad!

    Perhaps I should have better said "point closest", rather than equidistant, then there's only one possible point, rather than the infinite number on the perpendicular, as you correctly state!

    PS what part of the South Coast are you on? I'm in Hove.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Quote Originally Posted by RSDonovan View Post
    ...PS what part of the South Coast are you on? I'm in Hove.
    Perhaps this will give you a clue!

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Points Equidistant
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 3rd 2010, 03:44 PM
  2. Three Points Equidistant...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 19th 2010, 07:27 PM
  3. Replies: 1
    Last Post: May 12th 2010, 08:40 PM
  4. finding equidistant point
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 26th 2007, 10:13 AM
  5. equidistant points
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 13th 2006, 12:35 PM

Search Tags


/mathhelpforum @mathhelpforum