SOLUTION: prove that the triangle with vertices D(2,3), E(5,5), AND F(4,0) IS AN ISOSCELES, RIGHT TRIANGLE

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Question 186515: prove that the triangle with vertices D(2,3), E(5,5), AND F(4,0) IS AN ISOSCELES, RIGHT TRIANGLE
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
To show this we need to label the vertices p, q, and r, such that the vectors pq and pr are the same length and the angle between them is 90 degrees. This statement derives from an imaginary right isosceles triangle with the right angle at p.
If we let D=p, E=q, and F=r, then pq=(3,2) and pr=(2,-3). Both of these vectors have length 13^0.5, and they have a dot product of zero, meaning the angle between them is 90.