SOLUTION: Determine whether the given coordinates are vertices of a triangle. R(1,3),S(4,0),T(10,-6)

Question 550783: Determine whether the given coordinates are vertices of a triangle. R(1,3),S(4,0),T(10,-6)
Found 2 solutions by josmiceli, TutorDelphia:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If the slope from R to S is different
from the slope from S to T, then
The points cannot lie on the same
line, and they must form a triangle
----------
Slope R to S:

Slope S to T:

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The slopes are the same, so 2 line
segments joined together with the
same slope form a straight line, so
The 3 points do not make a triangle
Answer by TutorDelphia(193) (Show Source): You can put this solution on YOUR website!
A triangle is made up of three points that aren't all on the same line.

Looking at our three points we can see they are on a line. We can also determine that they are on a line by finding the equation of the lines or just by looking that all three points are along the same slope. From R to S our slope is 3/-3 and if we continue to add three to our y and subtract 3 to our x we get (7,-3) and then 10,-6 so we are along a line.
If you need a different kind of way to determine this, please specify.
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