Question

(5,7) (-5,-6) (5,-6)

Answer 1

(0, 0.5)

Explanation:

You want the circumcenter of the triangle defined by the points A(5, 7), B(-5, -6) and C(5, -6).

Right triangle

The fact that point C shares a coordinate with each of points A and B suggests the triangle is a right triangle. Graphing the points confirms this.

The circumcenter is the midpoint of the hypotenuse of that right triangle, so is ...

circumcenter = (A +B)/2

circumcenter = ((5, 7) +(-5, -6))/2 = (5-5, 7-6)/2 = (0, 1)/2

circumcenter = (0, 0.5)

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Answer 2

(0, 0.5)

Explanation:

Midpoint of BC: ([-5 + 5]/2, (-6 + (-6))/2) = (0, -6)

Perpendicular bisector of BC has equation: x = 0

Midpoint of AC: ([5 + 5]/2, (-6 + 7)/2) = (5, 0.5)

Perpendicular bisector of AC has equation y = 0.5

Point of intersection of the two perpendicular bisectors:

(0, 0.5)

Answer: (0, 0.5)