SOLUTION: 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)

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.

RELATED QUESTIONS
Determine whether the given coordinates are the vertices of a triangle. 1. A(3,5),... (answered by richwmiller,Edwin McCravy)

Determine whether the given coordinates are the vertices of a triangle. Explain. A(5, (answered by Fombitz)

Determine whether triangle PQR is congruent to triangle STU given the coordinates of the... (answered by ikleyn)

Determine whether the given coordinates are vertices of a triangle.... (answered by josmiceli,TutorDelphia)

Determine whether the given coordinates are vertices of a triangle.... (answered by solver91311)

Determine whether a figure with the given vertices is parallelogram. R(2, 3), S(-1, 2),... (answered by Fombitz)

1. The coordinates of the vertices of parallelogram ABCD are A(�1, �3), B(7, 2), C(5, 8), (answered by ewatrrr)

vertices of triangle STU are S(0,1) T(4,7) and U(8,-3) What are the coordinates of... (answered by solver91311)

Points R(1, 3), S(�2, �1), and T(5, �1) are vertices of a parallelogram. Give the... (answered by KMST)