show that the points (1,-1), (-1,1) ,(√3,√3) form an equilateral triangle
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ANSWER
Let A(1,1),B(−1,−1) and C(−√3,√3) be the vertices of ABC.
By distance formula, AB=
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
AB=
[(−1−1)
2
+(−1−1)
2
]
AB=
[(−2)
2
+(−2)
2
]
AB=
[4+4]
AB=
8
By distance formula,BC =
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
BC =
[(−√3−(−1))
2
+(√3−(−1))
2
]
BC =
[(−√3+1)
2
+(√3+1)
2
]
BC =
[3−2
3+1+3+2
3+1]
BC =
8
By distance formula, AC =
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
AC =
[(−√3−1)
2
+(√3−1)
2
]
AC =
[3+2
3+1+3−2
3+1]
AC =
8
Here AB=BC=AC.
So the points form an equilateral triangle.
Step-by-step explanation:
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