Question 421448: Determine whether the given coordinates are the vertices of a triangle. Explain.
problem #1. S(6,5), T(8,3), U(12,-1)
problem #2. D(1,-5), E(-3,0), F(-1,0)
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! Using the distance formula, 
I determined the distance between the points.
st = 2.8242
ut = 5.6568
su = 8.4852
By the triangle inequality thereom, the sum of any two sides of a triangle is > than the length of the third side.
adding st and ut, the result is < su. This would not fit the criteria for the vertexes of a triangle.
For the second set,
de = 6.4
ef = 4.0
fd = 5.4
This example does satisfy the triangle inequality thereom, it will be a valid triangle.
Cleomenius.
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