What are the coordinates of the circumcenter of a triangle with vertices a(−1,1), b(5,1), and c(−1,−1)? enter your answer in the boxes.

Circumcenter is (2,0)

Step-by-step 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)

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step-by-step explanation: