How do I determine whether a triangle with a given vertices is a right triangle? It gives...

(7,-1) (-3,5) (-12,-10)

you could see if the side lengths obey the Pythagorean Theorem. If it is a right triangle, it has to obey PT, but I am not sure if obeying the PT is necessary and sufficient for the triangle to be right, however...

 

The side lengths can be used in the trig relations, however, which would be necessary and sufficient for finding a 90* angle.

Edited August 28, 201114 yr by Bignose

I am not sure I understand =/

I've forgotten almost everything about triangles, I have area=1/2b+h and d=sqrt((x2-x1)+(y2-y1)). Not much else.

http://en.wikipedia.org/wiki/Pythagorean_theorem

Yeah I get that, I don't understand how to get A2+B2=C2 out of 3 points though.

you could see if the side lengths obey the Pythagorean Theorem. If it is a right triangle, it has to obey PT, but I am not sure if obeying the PT is necessary and sufficient for the triangle to be right, however...

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It is both necessary and sufficient. Sufficiency follows from the law of cosines.

It is both necessary and sufficient. Sufficiency follows from the law of cosines.

 

This is true that PT is sufficient but in the case when Three vertices r non colinear....

Can we call a line segment as a triangle with area zero??????????

It is both necessary and sufficient. Sufficiency follows from the law of cosines.

 

thanks, I thought so, but I wasn't sure.

This is true that PT is sufficient but in the case when Three vertices r non colinear....

Can we call a line segment as a triangle with area zero??????????

 

That would be the usual convention.

Yeah I get that, I don't understand how to get A2+B2=C2 out of 3 points though.

 

 

Well, you have 3 points. You have the formula of distance between points, so you have the lengths of three sides. If you can make those 3 sides fit into Pythagoras' Theorem, then you're done.