The labelled triangle is shown below
The required center is the point where the perpendicular bisectors meet. It is called the circumcenter. We would find it by applying the midpoint method. The midpoint formula is expressed as
midpoint, M(x, y) = (x1 + x2)/2, (y1 + y2)/2
For AB,
x1 = - 4, y1 = 0
x2 = 4, y2 = 0
Midpoint = (- 4 + 4)/2, (0 + 0)/2 = (0, 0)
For AC,
x1 = - 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (- 4 + 0)/2, (0 + 4)/2 = (- 2, 2)
For BC,
x1 = 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (4 + 0)/2, (0 + 4)/2 = (2, 2)
We woulf find the slope of AC
Slope, m = (y2 - y1)/(x2 - x1) = (4 - 0)/(0 - - 4) = 4/(0 + 4) = 4/4
m = 1
Slope of the line per