What are the coordinates of the circumcenter of this triangle?
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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).

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