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Without using Pythagoras theorem, show t...

Without using Pythagoras theorem, show that the points `A(0,4),\ B(1,2)a n d\ C(3,3)` are the vertices of a right angled triangle.

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Slope of AB =`(y_2-y_1)/(x_2-x_1)=(2-4)/(1-0)=-2`
Slope of BC= `(y_2-y_1)/(x_2-x_1)=(3-2)/(3-1)=1/2`
Slope of AB `xx` Slope of BC =-2 `1/2`=-1
Angle between AB and BC =`pi/2`
...
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