InterviewSolution
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InterviewSolution
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Show that the points A(1,2),B(1,6), `C(1 + 2sqrt(3),4) ` are the vertices of an equilateral triangle . |
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Answer» `A(1,2),B(1,6),C(1 + 2sqrt(3),4)` By distance formula , ` AB = sqrt((1 - 1)^(2) + (6-2)^(2))` ` therefore AB = sqrt(0^(2) + 4^(2))` ` therefore AB= sqrt(4^(2))` ` therefore AB = 4 ` `BC = sqrt((1 + 2sqrt(3)-1)^(2) + (4 -6)^(2))` ` therefore BC= sqrt((2sqrt(3)^(2) + )(-2)^(2))` ` therefore BC = sqrt(12 + 4)` ` therefore BC = sqrt(16) ` `therefore BC = 4` `therefore AC = sqrt((1 + 2sqrt(3)-1)^(2) + (4-2)^(2))` ` therefore AC = sqrt((2sqrt(3))^(2) + (2)^(2))` ` therefore AC = sqrt(12 + 4)` ` therefore AC = sqrt(16)` ` therefore AC = 4 ` ` therefore AB = BC = AC ` ` therefore Delta ABC ` is an equilateral triangle .i.e. the points A , B and C ar the vertices of an equilateral triangle . |
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