The coordinates of the circumcenter for ∆ABC A(0,0), B(4,0), C(4,-3)) are ((2, -1.5).
The coordinates of the circumcenter for Triangle ∆ABC with vertices A(-1,-2), B(-5,-2) and C(-1,-7) is (-3, -4.5).
How to calculate the circumcenter of triangle.
Given ∆sABC with vertices A(0,0), B(4,0) and C(4, -3) and A(-1,-2), B(-5,-2) and C(-1,-7).
To find the coordinates of the circumcenters of the follow the following steps.
Step 1:
For ∆ABC with vertices A(0,0), B(4,0) and C(4, -3),
let's find the midpoint of the lines.
Midpoint of AB = ((0 +4)/2, 0)
= (2,0)
Midpoint of BC = (4 + 4/2, -3 + 0/2)
= (4, -1.5)
Step 2:
Find the slope of the lines
Slope of AB = 0 - 0/4 - 0 = 0
Slope of BC = -3 - 0/4 - 4 = -3/0 = indeterminate.
Step 3:
Slope of perpendicular bisector of AB is undefined = -1/0.
Write equation of line AB
The equation of perpendicular bisector of AB is
x = 2
Since the slope of BC is undefined and the equation of the perpendicular bisector of BC is y = -1.5
The coordinates of the circumcenter is at
x = 2 and y = -1.5
So, the coordinates of the circumcenter for Triangle ABC A(0,0), B(4,0), C(4,-3)) are ((2, -1.5).
For ∆ABC with vertices A(-1,-2), B(-5,-2) and C(-1,-7).
Step 1:
Find the midpoint of the lines
Midpoint of AB = (-5 + (-1)/2, -2 + (-2)/2)
= (-3, -2).
Midpoint of BC = (-1 -5/2, -7 -2/2)
= (-3, -4.5)
Step 2:
Find the Slope of the lines
Slope of AB = -2 -(-2)/-5-(-1) = 0
Slope of BC = -7 +2/-1 +5 = -5/4
Step3:
The slope of perpendicular bisectors.
Slope of perpendicular bisector of AB, since the slope of AB = 0 , Slope of perpendicular bisector of AB is undefined.
The equation of perpendicular bisector is x = -3
Slope of perpendicular bisector of BC = 4/5.
Step 4:
Write the equation of the lines of perpendicular bisectors
Using the point (-3, -4.5)
The equation is y + 4.5 = 4/5(x + 3)
Solving x = -3 and y + 4.5 = 4/5(x + 3) together
x = -3, y = -4.5
So, the coordinates of the circumcenter for Triangle ∆ABC with vertices A(-1,-2), B(-5,-2) and C(-1,-7) is (-3, -4.5).