Yes, they are.   



Square of the distance between first two points:





Sum of squares of distances between 1st & 3rd and  2nd & 3rd points: 





So the triangle is a right triangle (with the right angle at (2,4))  

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 Determine if the points A(3,5), B(3,3) and C(2,4) are the vertices of a right triangle. Explain your rationale.

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Find the 3 side lengths

AB: d = 2

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BC: d = sqrt(2)

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AC: d = sqrt(2)

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AB is the longest

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Is AB^2 = BC^2 + AC^2 ??

2^2 = 2 + 2

4 = 4

It's a right triangle. 

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