find the circumcenter of the triangle (-3,3), (-3,-2), (1,-2)

Answer 1

The circumcenter is the intersection of the perpendicular bisectors of a triangle. We need to find the equations of two of those perpendicular bisectors and find the point where they intersect. That will be the circumcenter. For right triangles, the circumcenter will lie on the hypotenuse.

Equation of line between (-3,3) and (-3,-2) is x = -3 as it is a vertical line. The equation of the line that is the perpendicular bisector of that line is a horizontal line going through y = 1/2, the y coordinate that is the midpoint of that line.

Equation of line between (-3,-2) and (1,-2) is y = -2 as it is a horizontal line. The equation of the line that is the perpendicular bisector of that line is a vertical line going through x = -1, the x coordinate that is the midpoint of that line.

The intersection of those two lines will be at (-1,1/2), which lies on the hypotenuse.