We have a triangle defined by vertices M(0,6) N(8,0) O(0,0).
We have to find the circumcenter.
We can start by graphing the points:
We now have to calculate the midpoints of two of the segments.
We pick the segments OM and ON as they are easier to solve.
The midpoint of OM is (0/2,6/2)=(0,3).
The midpoint of ON is (8/2,0/2)=(4,0).
Now, we have to find the slope of the perpendicular lines to each segment.
As OM is a vertical line, the perpendicular line has a slope of 0 (horizontal line)
For the segment ON, as it is an horizontal line, the slope of the perpendicular line, as it is a vertical line, has an infinite value.
We then have to define the perpendicular lines that pass through the midpoints.
For OM, we have a horizontal line that pass through (0,3), so the equation is y=3.
In the case of ON, the vertical line pass through (4,0), so it has an equation x=4.
We can graph this as:
The intersection point for the two bisector lines x=4 and y=3 is the circumcenter, that is located at point (4,3).