Question

A(root2,root2),B(-root2,-root2),C(-root6,root6)​

Answer 1

A(root2,root2),B(-root2,-root2),C(-root6,root6)​

Question is : given are the three vertics of an triangle

what kind of triangle is this ?

Ans

A (√2 , √2)

B (-√2 , -√2)

C (-√6 , √6)

AB² = (-√2 - √2)² + (-√2 - √2)² = (-2√2)² + (-2√2)² = 8 + 8 = 16

=> AB = √16 = 4

BC² = (-√6 - (-√2))²  + (√6 - (-√2))² =  (-√6 +√2))²  + (√6 + √2))²

=> BC² = 6 + 2 - 2√6√2 + 6 + 2 + 2√6√2 = 16

=> BC = √16 = 4

AC² = (-√6 - √2))²  + (√6 - √2))²

=> AC² = 6 + 2 + 2√6√2 + 6 + 2 - 2√6√2 = 16

=> AC = √16 = 4

AB = BC = AC = 4

All sides are equal

so triangle is equilateral