Question

What are the coordinates of the circumcenter of a triangle with vertices A(−1, 1) , B(5, 1) , and C(−1, −1) ?

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Answer 1

A right triangle in a circumcircle is always in the semicircle, with the centre of the circle lying in the middle of the side opposite the right angle.

So, the circumcenter is the midpoint of BC.

The midpoint of BC is ((5-1)/2, (1-1)/2) = (2, 0)

Explanation:

Answer 2

Triangle ABC is a right triangle with vertex A containing the right angle.

You can tell because AB is a horizontal line since A and B have the same y-coordinate, and AC is a vertical line since A and C have the same x-coordinate.

A right triangle in a circumcircle is always in the semicircle, with the centre of the circle lying in the middle of the side opposite the right angle.

So, the circumcenter is the midpoint of BC.

The midpoint of BC is ((5-1)/2, (1-1)/2) = (2, 0)