MaplePrimes - answers and comments on Question, orthocenter of the triangle

My comment

Kitonum — Thu, 19 Jan 2012 14:52:38 Z

Your code is correct, but too long.

Another solution:

restart:

with(LinearAlgebra):

A:=<1,-3,0>: B:=<-2,1,1>: C:=<3,1,2>: M:=x*A+y*B+z*C:

{DotProduct(B-A,C-M)=0, DotProduct(C-A,B-M)=0, x+y+z = 1}:

solve({DotProduct(B-A,C-M)=0, DotProduct(C-A,B-M)=0, x+y+z = 1}): assign(%): M:

'M'=[seq(M[i],i=1..3)];

M=[4/5, -2/5, 1]

How to find the barycentric coordinates of the ort...

JAMET — Thu, 08 Aug 2024 07:17:17 Z

How to find the barycentric coordinates of the orthocenter of the ABC triangle (in the ABC repere) using cartesian coordinates ? Thank you..

Re

Kitonum — Thu, 08 Aug 2024 16:36:26 Z

@JAMET See code below. x, y, z are the barycentric coordinates of point M:

restart;
with(LinearAlgebra):
A:=<1,-3,0>: B:=<-2,1,1>: C:=<3,1,2>: M:=x*A+y*B+z*C:
{DotProduct(B-A,C-M)=0, DotProduct(C-A,B-M)=0, x+y+z = 1}:
solve({DotProduct(B-A,C-M)=0, DotProduct(C-A,B-M)=0, x+y+z = 1}); # barycentric coordinates of M
'M'=eval(M, %); # cartesian coordinates of M

Can you explain M:=xA+yB+z*C and x+y+z

toandhsp — Thu, 19 Jan 2012 19:59:12 Z

Can you explain M:=x*A+y*B+z*C and x+y+z = 1. I don't understant. Thank you.

Higher dimensions

Markiyan Hirnyk — Thu, 19 Jan 2012 20:14:27 Z

The approach used by Kitonum works in higher dimensions (>3) too.

Explanation

Kitonum — Thu, 19 Jan 2012 20:43:01 Z

If three points A, B and C are collinear, they define a single plane, and each point M of this plane is given by the formula M = xA + yB + zC, where x + y + z = 1. The numbers x, y, z are called the barycentric coordinates of the point M.