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Question

If (0, 0), (3, 0) and (x, y) are the vertices of an equilateral triangle, then the value of x and y is

A
(32,332)or(32,332)
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B
(12,2)or(12,2)
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C
(13,1)or(13,1)
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D
none of these
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Solution

The correct option is A (32,332)or(32,332)
LetustaketheequilateralΔasAOBwithA=(x,y),B=(3,0),O=(0,0).TheordinatesofB&Oare=0.SoBOliesontheXaxis.Also(AB=BO&AO=BO).................(i)[sinceΔAOBisequilateral]ThelengthBO=30=3.........(ii)NowAB=(3x)2+(0y)2=x2+y26x+9=3[from(i)]x2+y26x=0.............(iii)AgainAO=(0x)2+(0y)2=3[from(i)]x2+y2=9................(iv)From(i)&(iv)wehave96x=0x=32Substitutingx=32in(iv),y=±332(x,y)=(32,332),(32,332)AnsOptionA

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