two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex
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Step-by-step explanation:
Let ABC be the equilateral triangle such that,
A=(3,0),B=(6,0) and C=(x,y)
Distance formula:
√{(x2-x1)^+(y2-y1)^2}
we know that ,
AB=BC=AC
By distance formula we get,
AB=BC=AC=3units
AC=BC
√{(3-x)^2+y^2}=√{(6-x)^2+y^2}
9+x^2-6x+y^2=36+x^2-12x+y^2
6x=27
x=27/6=9/2
BC=3units
√{(6-27/6)^2+y^2}=3
{(36-27)/6}^2+y^2=9
(9/6)^2+y^2=9
(3/2)^2+y^2=9
9/4+y^2=9
9+4y^2=36
4y^2=27
y^2=27/4
y=√(27/4)
y=3√3/2
(x,y)=(9/2,3√3/2)
Hence third vertex of equilateral triangle=C=(9/2,3√3/2)
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