Answer:
The coordinate of the circumcenter of the given triangle is (4, -1)
Step-by-step explanation:
The circumcenter is found by the intersection of the perpendicular bisectors of a triangle as follows;
The vertices of triangle ΔABC are A(1, 1), B(1, -3), and C(7, -3)
The coordinates of the midpoint of segment AB is 1/2(1 + 1, 1 + (-3)) = (1, -1)
The slope of segment AB = ∞, therefore, the slope of the perpendicular to segment AB = -1/∞ = 0
The line representing the perpendicular to segment AB is y = -1
The coordinates of the midpoint of segment BC is 1/2(1 + 7, (-3) + (-3)) = (4, -3)
The slope of segment BC = 0, therefore, the slope of the perpendicular to segment BC = ∞, which is a vertical line parallel to the y-axis with equation, x = 4
Therefore, the coordinate of the circumcenter is the intersection of the lines y = -1, and x = 4, which is the point (4, -1).
