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Question

The coordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1,0) and (2,0), respectively. Then the equation of the diagonal CE is

A
3x+y=4
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B
x+3y+4=0
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C
x+3y=4
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D
x3y=4
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Solution

The correct option is C x+3y=4

Sum of interior angles =(62)180=720
Each interior angle of the hexagon is 120.
CBX=60
BC makes an angle 60 with xaxis.
Length of side of hexagon is 1 unit.
Using parametric form,
C(2+1cos60,0+1sin60)
C(52,32)

Coordinates of E are (1,2×sin60)=(1,3)
Hence, equation of the diagonal CE is
y3=323521(x1)
i.e., x+3y=4

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