ABC is a equilateral triangle with coordinates of B (1,0) and C(5,0). Find the co-ordinates of vertex A. (Can you please explain how to do this type questions.)

Hello student,
Please find the answer to your question below
Givencoordinates of B (1,0) and C(5,0)
Let coordinates of A be (a,b)
In an equilateral triangle the lengths of all sides will be equal
So BC==4
So AB=CA=4
AB==4
Squaring on both sides we get
(a-1)²+b²=16
a²+b²-2a-15=0.......(1)
Also CA==4
Squaring on both sides we get
(5-a)²+b²=16
a²+b²-10a+9=0........(2)
(1)-(2) gives we get 8a-24=0
So a=3
Substituting a=3 in equation 1 we get b²=12 So b=2
So vertex A is (3,2)