Question

If two vertices of an equilateral
triangle are (1,0) and (4,0), find the
third vertex.​

Answer 1

Answer:

third vertex is (5/2, 3√3/2)

Step-by-step explanation:

given, A(1,0), B(4,0)

let third vertex be C(x, y)

As we know triangle is equilateral triangle

so, AC=BC=AB

AB=√(4-3)^2+(0-0)^2=3 equation 1

BC=√(x-4)^2+(y-0)^2=√(x-4)^2+y^2 equation 2

AC=√(x-1)^2+(y-0)^2=√(x-1)^2+y^2 equation 3

by solving equations 1,2 and 3 we will get x, y

x=5/2 and y=3√3/2

so the vertex is C(5/2,3√3/2)