Question

if 2 vertices of a equilateral triangle are (3,0) ,(6,0). find the 3rd vetex.

Answer 1

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^26x=27x=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
=99/4+y^2
=99+4y^2
=364y^2
=27y^2
=27/4y
=√(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)
hope it helps you 
all the best
do mark brainlist