Question

What are the coordinates of the circumcenter of this triangle?

Answer 1

The answer is (3,2) because i had that question on my test.

Answer 2

Answer: The circumcenter of this triangle is (3, 2).

Explanation:

Since, circumcenter is the center of the circle which passes through all the vertices of the triangle.

Here, $\triangle ABC$ is a right angle triangle, and, in the case of right angled triangle the circumcenter is the midpoint of the hypotenuse.

In $\triangle ABC$, AC is the hypotenuse,  where A≡(-2,5) and C≡(8,-1)

So, the coordinates of the mid points = $(\frac{-2+8}{2},\frac{5-1}{2})= (\frac{6}{2},\frac{4}{2})=(3,2)$

So, the circumcenter of $\triangle ABC$ = (3,2)