Question

show that the following points form a equilateral triangle A(a, 0), B(-a, 0), C(0, a√3)​

Answer 1

Answer:

It is proved to be an equilateral triangle, by showing that the length of all the three sides are equal.

Explanation:

length of side AB:

= √((a - -a)² + (0-0)²)

= √(2a)²

= 2a

length of side BC:

= √((a√3 - a)² + a²)

= √(3a² + a² -2√3a² + a²)

= √(4a²)

= 2a

length of side CA:

= √(a² + 3a²)

= √(4a²)

= 2a

Since,

length of side AB = length of side BC = length of side CA

hence proved, it is an equilateral triangle.