Asked by hannah
The vertices of triangle ABC are A(2,2), B(3,-1) and C(0,1). Find the coordinates of the circumcenter. Answer choices:(23/14,3/14), (3/2,0) or (7/9,11/9)
Answers
Answered by
Reiny
the circumcentre lies on the intersection of the right-bisectors of any two chords.
lets use chords BC and AC
midpoint of AC is (5/2,1/2)
slope of AC is -3
so slope of right-bisector is 1/3
equation of right-bisector is
y-1/2 = (1/3)(x-5/2)
times 3
3y - 3/2 = x - 5/2
times 2
6y - 3 = 2x - 5
2x - 6y = 2
x - 3y = 1 (#1)
now repeat this to find right-bisector of BC, call it #2
solve #1 and #2
see if you can get (23/14,3/14), that's what I got.
lets use chords BC and AC
midpoint of AC is (5/2,1/2)
slope of AC is -3
so slope of right-bisector is 1/3
equation of right-bisector is
y-1/2 = (1/3)(x-5/2)
times 3
3y - 3/2 = x - 5/2
times 2
6y - 3 = 2x - 5
2x - 6y = 2
x - 3y = 1 (#1)
now repeat this to find right-bisector of BC, call it #2
solve #1 and #2
see if you can get (23/14,3/14), that's what I got.
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