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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x+√3y+4=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x+√3y=4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x−√3y=4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Cx+√3y=4
Sum of interior angles =(6−2)180∘=720∘
Each interior angle of the hexagon is 120∘. ∴∠CBX=60∘ BC makes an angle 60∘ with x−axis.
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 y−√3=√32−√352−1(x−1)
i.e., x+√3y=4