Answer:
Circumcenter is (2,0)
Explanation:
We have been given three vertices of a triangle A(-1,1), B(5,1) and C(-1,-1)
The triangle formed by these vertices is a right angle triangle you can see the attachment for the figure
To Prove the vertices form right angle triangle we can satisfy the pythagoras theroem which says that square of hypotenuse is equal to sum of square of sides.
Here hypotenuse Hypotenuse is BC which is the longest side
Hence

Hence find the distance of BC using distance formula which is

Substituting the value B(5,1) and C(-1,-1) in the distance formula
we will get




Similarly, we will find AB with
we will get


Similarly, we will find AC
Here,
substituting values in the formula we will get



Hence,

Implying the triangle is right angle triangle
And circumcenter of right angle triangle is mid point of hypotenuse.
Now, we will find midpoint of hypotenuse that is midpoint of BC

Here,

On substituting the values in the formula we will get


Hence, circumcenter is (2,0)