(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A, B, C, D be the vertices of a convex quadrilateral. Convexity means that for each lines L(ab), L(bc), L(cd), L(da) the quadrilateral lies in one of its half-planes. Find the point P for which the minimum Min(d(P,A)+d(P,B)+d(P,C)+d(P,D)) is realized.

2. Relevant equations

Min(d(P,A)+d(P,B)+d(P,C)+d(P,D)) is the equation we're trying to minimize.

distance=d(X,Y)=abs(X-Y)=sqrt((X-Y)x(X-Y)) where "x" is the dot product.

3. The attempt at a solution

For starters, this is for my Euclidean geometry class, so there's no coordinates or Calculus, I presume. My initial guess is that the point that would minimize those distances would be the intersection of the diagonals but I can't figure out why.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Minimum distance in within a quadrilateral

**Physics Forums | Science Articles, Homework Help, Discussion**