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Question

A(2,2) , B(-2,-2),C(-2√3,2√3) . Show that the following points take in order form an equilateral triangle ?

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Solution

Solution:

A = (2,2)
B = (-2,-2)
C = (-2√3,2√3)

AB =√[(2-(-2)]²+[(2-(-2)]²
= √16+16
= √32
= 4√2

BC=√[-2√3-(-2)]²+[2√3-(-2)]²
= √(-2√3+2)²+(2√3+2)²
= √(1-√3)².2²+(√3+1)².2²
= 2√[ 1+3-2√3+3+1+2√3]
= 2√8
= 4√2

CA =√[-2√3-(2)]²+[2√3-(2)]²
= √(-2√3-2)²+(2√3-2)²
= √(-√3-1)².2²+(√3-1)².2²
= 2√[3+1+2√3+3+1-2√3]
= 2√8
= 4√2

∴AB = BC = CA
It forms an eqilateral traingle.
(Proved)
(Answer)

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