Answer:
Step-by-step explanation:
The circumcenter is the intersection of the perpendicular bisectors.
Find the two equations for the perpendicular bisectors and solve the system for intersection point.
Given the vertices A(-4,6), B(6,6), C(6,2)
Find the slope and midpoint of AB and BC
- m(AB) = (6 - 6)/(6 - (-4)) = 0, this is a horizontal segment
M(AB) is
- x = (-4 + 6)/2 = 1, y = (6 + 6)/2 = 6
Perpendicular bisector is a vertical line that passes through (1, 6) so its equation is:
m(BC) is undefined as x-coordinates are same, so the segment is vertical
M(BC) is
- x = (6 + 6)/2 = 6, y = (6 + 2)/2 = 4
Perpendicular bisector is a horizontal line that passes through (6, 4) so it is:
The intersection of the lines x = 1 and y = 4 is the point (1, 4)
The circumcenter is point (1, 4)
