What are the coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1) , and C(2, 5) ?Enter your answer in the boxes(__,__)

Answer: The coordinates of circumcenter is (1,3).Explanation:It is given that the triangle have vertices A(0,1), B(2, 1) , and C(2, 5).The distance formula,[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]AB=\sqrt{(2-0)^2+(1-1)^2}=2[/tex][tex]BC=\sqrt{(2-2)^2+(5-1)^2}=4[/tex][tex]AC=\sqrt{(2-0)^2+(5-1)^2}=\sqrt{20}[/tex]Since,[tex](AC)^2=(AB)^2+(BC)^2[/tex]By pythagoras we can say that the given triangle is a right angle triangle and AC is the hypotenuse of the triangle.The circumcentre of a right angle triangle is the midpoint of the hypotenuse.Midpoint of AC,[tex]\text{Midpoint of AC}=(\frac{0+2}{2}, \frac{1+5}{2})[/tex][tex]\text{Midpoint of AC}=(\frac{2}{2}, \frac{6}{2})[/tex][tex]\text{Midpoint of AC}=(1,3)[/tex]Therefore, the coordinates of circumcenter is (1,3).