Question

Find the coordinates of the circumcenter of the triangle with the given vertices.

A(0, 0), B(0, 8), C(6, 0)
The circumcenter is

Answer 1

The coordinates of the circumcenter of triangle ABC are (1, 2).

Step-by-step explanation:

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the coordinates of the circumcenter, we need to find the midpoint of each side and then find the slopes of the perpendicular bisectors. The point where the perpendicular bisectors intersect is the circumcenter.

1. First, find the midpoint of AB which is (0, 4).
2. Then find the slope of AB, which is undefined since the line is vertical.
3. Next, find the midpoint of BC which is (3, 0).
4. Find the slope of BC, which is 1/3.
5. Lastly, find the midpoint of AC which is (3, 4).
6. Find the slope of AC, which is -3.
7. Now we have two equations of perpendicular bisectors: y = 3x - 8 and y = -x + 7/2. Solving these equations gives us the point of intersection, which is (1, 2).

Therefore, the coordinates of the circumcenter of triangle ABC are (1, 2).