show that the pointA(1,2),B(1,6),C(1+2√4)are vertexan equilateral triangle
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Explanation:
Answer
Given A(1,2)B(1,6)C(1+2
3
,4)
using distance formula
AB=
(1−1)
2
+(6−2)
2
=
4
2
=4
BC=
(1+2
3
−1)
2
+(4+6)
2
=
12+4
=4
CA=
(1−1−2
3
)
2
+(2−4)
2
=
12+4
=4
Since AB=BC=CA
∴ ABC is an equilateral triangle
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