Find the coordinates of the circumcenter for triangledef with coordinates d(1,1) e(7,1) and f (1,5). show your work.

1. plot the points in the coordinate axis. Check the picture.

2. The circumcenter of a triangle is the center of the circumscribed triangle.

3. To find the circumcenter we draw the perpendicular bisector of each side, that is the line segments which are perpendicular to the sides, and divide each ith them in 2 equal parts.

4. Since all 3 perpendicular bisectors meet at the circumcenter, it is enough to draw 2 of them, as shown in the picture.

5. with our construction, we find the center O(4, 3)

Another way to solve this problem is to notice than the triangle is a right triangle. The circumcircle of a right triangle has the hypotenuse as a diameter. So it is enough to find the midpoint of FE.

(4, 3)