Question

Show that the points (a. a). (-a, -a) and (-root 3a, root 3a) are the vertices of an equilateral triangle.

SUPER URGENT PLS!!!!

Answer 1

A = (a,a)
B = (-a,-a)
C = (-√3a,√3a)
AB=√(-a-a)²+(-a-a)²
       √4a²+4a²
         √8a²
         2√2 a
BC=√(-√3a+a)²+(√3a+a)
        √(1-√3)²a²+(√3+1)²a²
        a√[ 1+3-2√3+3+1+2√3]
        a[ √8]
        2√2a
CA = √(-√3a-a)²+(√3a-a)²
         √(-√3-1)²a²+(√3-1)²a²
         a√[3+1+2√3+3+1-2√3]
         a√8
         2√2a
∴AB = BC = CA
  it forms a eqilateral traingle
 

Answer 2

Answer:

Step-by-step explanation: