# Thread: The place: Distance and measurement

1. ## The place: Distance and measurement

Find a poing inside a convex quadrilateral such that the sum of the distances from the point to the vertices in minimal.

How would I show that a distance that I find is indeed minimal? I'm kinda just confused as to how to even start this...

Thank you!

2. Put a convex quadrilateral on a Cartesian coordinate system.
Put a point inside.
Calculate the total distance to all four corners.
Ponder the outcome.

3. but how would I PROVE it?

4. Wouldn't it just be the intersection of the diagonals?

The diagonals are the shortest distance from one vertex to another, so I think the point of intersection would be the shortest distance from each vertex.

5. ahh so ould it then just be sufficient to say "since the diagonals are the shortest distance from vertice to vertice its intersection is the shortest to each point?"

And thank you!

6. You can say that, but that doesn't constitute a proof. Pick another point and prove it.