Answer:
The answer to your question is (2, -1)
Step-by-step explanation:
1.- Find half points
AB
Between A and B there are 6 units, then the half point is three units from point A to the right
(2, 3)
BC
Between B and C there are 8 units, then the half point is four units below the point B.
(5, -1)
AC
Xm = -1 + 5 / 2 = 4 / 2 = 2
Ym = 3 - 5 / 2 = - 2 / 2 = - 1
(2, -1)
2.- Find the equations of the mediatrices
AB
x = 2 because the line must be perpendicuar to AB
BC
y = - 1 because the line must be perpendicular to BC
AC
slope m =[tex]\frac{-5 - 3}{5 + 1}[/tex]
m = [tex]\frac{-8}{6}[/tex]
m = [tex]\frac{-4}{3}[/tex]
mediatrix AC
y + 1 = -4/3 (x -2)
3y + 3 = -4x + 8
4x + 3y = 8 - 3
4x + 3y = 5
3.- Find the circumcenter
When x = 2
4(2) + 3y = 5
8 + 3y =5
3y = 5 - 8
3y = -3
y = -3/3
y = -1
When y = -1
4x + 3(-1) = 5
4x - 3 = 5
4x = 5 + 3
4x = 8
x = 8/4
x = 2
Circumcenter (2, -1)
