Question

Find the circumcenter of a triangle with the given vertices: o(0, 0), K(0, 12), L(4, 0)

A) (2, 6)
B) (0, 6)
C) (2, 0)
D) (4, 6)

Answer 1

The circumcenter of a right-angled triangle is at the midpoint of the hypotenuse. For triangle OKL, the circumcenter is at (2, 6), which is option A.

Step-by-step explanation:

To find the circumcenter of a triangle with vertices O(0, 0), K(0, 12), and L(4, 0), we must identify the point that is equidistant from all three vertices. Since triangle OKL is a right-angled triangle with the right angle at vertex O, the circumcenter will lie at the midpoint of the hypotenuse KL. The midpoint of KL can be found by averaging the x-coordinates and y-coordinates of K and L, respectively.

The midpoint of KL (x-coordinate): (0 + 4) / 2 = 2
The midpoint of KL (y-coordinate): (12 + 0) / 2 = 6

Therefore, the circumcenter is at coordinate (2, 6), which is option A.