Answer:
-2 in the first box
2 in the second box
In other words, the circumcenter is located at (-2, 2). Do not type in the parenthesis.
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Step-by-step explanation:
Points A and C are (2,-3) and (-6,-3) in that order.
Use the midpoint formula to find that M = (-2,-3) is the midpoint of segment AC. It is halfway between these endpoints.
The perpendicular bisector to segment AC is x = -2
The perpendicular bisector goes through the midpoint, and it is perpendicular to segment AC.
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Points A and B are (2,-3) and (2,7) respectively.
The midpoint is at N = (2,2)
The perpendicular bisector of segment AB is the equation y = 2.
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We found the following:
- The perpendicular bisector to segment AC is x = -2
- The perpendicular bisector to segment AB is y = 2
Therefore, the circumcenter is located at (-2, 2) as the circumcenter is located at the intersection of the perpendicular bisectors.
The diagram is shown below. As the diagram shows, the circumcenter marked in red is the center of the circle that goes through points A, B, and C.
Side note: The circumcenter is located on the midpoint of the hypotenuse of any right triangle. See Thales theorem.