Question

Circumcenter of triangle with vertices of (1,1) (1,-3) (7,-3)

Answer 1

Answer:

The circumcenter is (-17/2, -15/2)

Step-by-step explanation:

To find the circumcenter, solve any two bisector equations and find out the intersection points. The given are A(1,1), B(0,2), and C(3,-2).Midpoint of AB = (1/2, 3/2)  - You can get the midpoint by getting the average of x-coordinates and y-coordinates. Slope of AB = -1Slope of perpendicular bisector = 1Equation of AB with slope 1 and the coordinates (1/2, 3/2) isy - (3/2) = (1)(x - 1/2) y = x+1Do the same for ACMidpoint of AC = (2, -1/2)Slope of AC = -3/2Slope of perpendicular bisector = 2/3Equation of AC with slope 2/3 and the coordinates (2, -1/2) isy - (-1/2) = (2/3)(x - 2) y = -11/6 + 2x/3So the perpendicular bisectors of AB and BC meety = x+1y = -11/6 + 2x/3To solve for x,(-11/6 + 2x/3) = (x+1)x= -17/2Now get y by substituting y = (-17/2) + 1y = -15/2