Patrick B. answered • 29d

Math and computer tutor/teacher

midpoint of PQ is (1,3); slope of PQ is 4/-6 = -2/3, which means the perpendicular bisector has slope 3/2

so the perpendicular bisector of PQ has intercept B = y - mx = 3 - (3/2)(1) = 3 - 3/2 = 3/2

the perpendicular bisector of PQ is then y = (3/2)x + 3/2

midpoint of QR is (1,-1); slope of QR is 4/6 = 2/3, which means the perpendicular bisector has slope -3/2

so the perpendicular bisector of QR has intercept B = y - mx = -1 - (-3/2)(1) = -1 + 3/2 = 1/2

the perpendicular bisector of QR is then y = (-3/2)x + 1/2

midpoint of PR is (-2,1); slope of PR is undefined.

so the perpendicular bisector of PR is y = 1

(3/2)x + 3/2 = (-3/2)x + 1/2

(6/2)x + 3/2 = 1/2

3x + 3/2 = 1/2

3x = -1

x = -1/3

which forces y = (3/2)(-1/3) + 3/2 = -1/2 + 3/2 = 1

y = (-3/2)(-1/3) + 1/2 = 1

the circumcenter is (-1/3,1)