Find the circumcenter of triangle ABC. A is at (2,5), B is at (2,3) and C is located at (6,3).(1 point)
To find the circumcenter of triangle ABC, we first find the slopes of the perpendicular bisectors of two of its sides.
The slope of the perpendicular bisector of side AB can be found by taking the negative reciprocal of the slope of AB:
Slope of AB: (3 - 5) / (2 - 2) = undefined (division by zero)
Since the slope of AB is undefined, the line perpendicular to AB is a vertical line passing through the midpoint of AB, which is the point (2, 4).
Similarly, the slope of the perpendicular bisector of side BC can be found:
Slope of BC: (3 - 3) / (6 - 2) = 0
Since the slope of BC is 0, the line perpendicular to BC is a horizontal line passing through the midpoint of BC, which is the point (4, 3).
The intersection of these two perpendicular bisectors is the circumcenter of triangle ABC. Since one of the lines is vertical and the other is horizontal, their point of intersection is (2, 4).
Therefore, the circumcenter of triangle ABC is located at (2, 4).