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Proof by deduction

“prove that A,Band C are the vertices of a right angled triangle”
The coordinates of A,B and C are given and the book solves it by finding the grad of AB, grad of BC and proving they are perpendicular but my question is could I find the distances between each vertice and prove it using Pythagoras?
(edited 1 month ago)
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Original post by olygilly
“prove that A,Band C are the vertices of a right angled triangle”
The coordinates of A,B and C are given and the book solves it by finding the grad of AB, grad of BC and proving they are perpendicular but my question is could I find the distances between each vertice and prove it using Pythagoras?
Yes, though its probably slightly less work to do as the book does.

The cos rule is the more general form and showing c^2=a^2+b^2 is equivalent to showing cos(C)=0 so C=pi/2. You could also have done Thales, so every vertex is the same distance from the centre of the hypotenuse.
(edited 1 month ago)

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