Question

If 2 vertices of an equilateral triangle ABC are A (3,0) B(6,0). FInd the third vertex

Answer 1

AB is =
$\sqrt{ {(3 - 6)}^{2} + {(0 - 0)}^{2} }$
=√(-3)²
=√9=3
let the vertex of C is (x,y)
then AC is =
$\sqrt{ {(x - 3)}^{2} + {(y - 0)}^{2} }$
...........................(1)
then BC is =
$\sqrt{ {(x - 6)}^{2} + {(y - 0)}^{2} }$
...........................(2)
then
(1)=(2)
or (x-3)²=(x-6)²
or x²-6x+9=x²-12x+36
or 6x=27
or x=4.5

again (1)=3
so (x-3)²+y²=9
or (4.5-3)²+y²=9
or (1.5)²+y²=9
or y²=9-2.25
or y²=6.75
or y²=(25*27)/100
or y=(+-)(3√3/2)
then vertex of C may
(4.5,3√3/2) or may (4.5,-3√3/2)