Prove that the points(3,0),(6,4)and(-1,3) are vertices of right angled isosceles triangle.........

Prove that the points(3,0),(6,4)and(-1,3) are vertices of right angled

1.	Prove that the points(3,0),(6,4)and(-1,3) are vertices of right angled isosceles triangle.........
Answer» Given A(3, 0), B(6, 4) and C(-1, 3)AB2\xa0= (3 - 6)2\xa0+ (0 - 4)2\xa0= 9 + 16 = 25BC2\xa0= (6 + 1)2\xa0+ (4 - 3)2\xa0= 49 + 1 = 50CA2\xa0= (-1 - 3)2\xa0+ (3 - 0)2\xa0= 16 + 9 = 25AB2\xa0= CA2\xa0or, AB = CATriangle is isocelesAlso, 25 + 25 = 50or, AB2\xa0+ CA2\xa0= BC2Since, pythagoras theorem is verified, therefore triangle is right-angled triangle.