1. Limited time only! Sign up for a free 30min personal 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!

Center mass of triangle in 3-D space

  1. Sep 6, 2011 #1
    1. The problem statement, all variables and given/known data
    So I have a triangle with points: A (4,2,0), B (3,3,0), and C (1,1,3). We are to find the point at which the three medians intersect in i,j,k format. I've found the midpoints of each side but I don't know where to go from there.
     
  2. jcsd
  3. Sep 6, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Construct the equation of the line joining the midpoint and the opposite vertex. Do this for all vertices.
     
  4. Sep 6, 2011 #3

    dynamicsolo

    User Avatar
    Homework Helper

    You can save a good bit of this work if you are allowed to use the theorem which states that the medians of a triangle intersect at a point with divides each median in the ratio of 2:1 . Then you can choose any one median and find the point (by proportions) which is one-third of the way from the base to the opposite vertex. (Any other choice of a median to work with should give exactly the same result.)

    I am presuming in this that the problem is not asking you to show that all three medians meet at the point with this property.
     
  5. Sep 6, 2011 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The simplest way to do this: the coordinates of the centroid of a triangle (not, strictly speaking, the "center of mass" because a geometric figure does not have 'mass') is the mean of the coordinates of the three vertices. That is, if the vertices of the triangle are at [itex](x_1, y_1, z_1)[/itex], [itex](x_2, y_2, z_2)[itex], [itex](x_3, y_3, z_3)[/itex], then the centroid is at
    [tex]\left(\frac{x_1+ x_2+ x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)[/tex]

    If you don't have that theorem, use that as a check.
    (The average of the coordinates works for the two dimensional triangle or three dimensional tetrahedron but not for other figures.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Center mass of triangle in 3-D space
  1. Mass of a triangle (Replies: 4)

  2. Center of mass (Replies: 1)

Loading...