Posted by Soroban on September 02, 2002 at 19:19:07:
In Reply to: Re: Triangle Inequality Essay posted by Brad Paul on September 02, 2002 at 16:13:16:
: : Here's the question:
: : "Explain in general how the Triangle Inequality might be applied in order to determine whether 3 points are collinear. Back up your explanation with a specific application."
: : I have no clue. Any help?
: Imagine a triangle with an area greater than zero. Now push one vertex
: onto the opposite side. At this point the "triangle" has zero area,
: the vertexes are collinear, and the Triangle Inequality is satisfied with
: an equality.
Kirby, Brad is correct.
In a "normal" triangle (that is, there is a triangle), the sum
of any two sides is always greater than the third side.
If they give us a "triangle" with sides 3, 4, 7,
we find that 3 + 4 is NOT greater than 7.
In fact, 3 + 4 is EQUAL to 7, the third side.
And THAT would be a test for collinear points.
Something like "Given three points and the distances
between them, if the sum of two distances equals the third,
the points are collinear."
Maybe you can polish it up.
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