Question

★show that the points:
A (a, a) ,B(-a, a), C (-a√3, a√3)
we need to show that these points that an equilateral triangle.​

Answer 1

Answer:

Given: A = (a, a), B = (-a, a), C = (-a√3, a√3)

AB = $\sqrt{(-a-a)^2+(-a-a)^2}$

     = $\sqrt{4a^2 + 4a^2} = 2\sqrt{2}a$ $units$

BC = $\sqrt{(-a\sqrt{3} +a)^2} + \sqrt{(a\sqrt{3} +a)^2}$

     = $\sqrt{3a^2 + a^2 - 2\sqrt{3}a^2 + 3a^2 + a^2 + 2\sqrt{3}a^2 }$

= √8a² = 2√2a units

AC = $\sqrt{a\sqrt{3}-a^2} + \sqrt{a\sqrt{3}-a^2$

     = $\sqrt{3a^2+a^2-2\sqrt{3}a^2 + 3a^2 + a^2+ 2\sqrt{3}a^2$

=  √8a² = 2√2a units

∴ AB = BC = AC = 2√2a

Hence, ΔABC is an Equilateral.

Hence Proved