Q. 24.8( 5 Votes )

Prove that by joining the point (2, 1), (3, 4), (– 3, 6) we get a right triangle.

Answer :

Let A = (2,1)


B = (3,4)


C = (– 3,6)


Length of Side


AB = distance between point A and B =


Here x2 = 3,y2 = 4,x1 = 2,y1 = 1


AB =


AB =


AB =


AB = √10 units


BC = distance between point B and C =


Here x2 = – 3,y2 = 6,x1 = 3,y1 = 4


BC =


BC =


BC =


BC = √40units


CA = distance between point C and A =


Here x2 = 2,y2 = 1,x1 = – 3,y1 = 6


CA =


CA =


CA =


CA = √50 units


Here CA is the largest side.


For ΔABC to be right angled triangle



Here,



And



50 = 50



the given triangle is a right – angled triangle.


Hence Proved.


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