Question

FInd the circumcenter of the triangle (-2,4),(-2,1), (1,-1). Can someone help I'm so confused.

Answer 1

for this, you need to recall that the perpendicular bisector of a chord goes through the center of the circle.

So, if you can find two of the bisectors, they will intersect at the center.

To find the bisectors, locate the midpoint of a chord, then find a line perpendicular to the chord that goes through that point.

If we call the points A,B,C, then
mid(AB) = (-2,5/2)
mid(AC) = (-1/2,3/2)
mid(BC) = (-1/2,0)

slope(AB) = ∞
slope(AC) = -5/3
slope(BC) = -2/3

So, we need lines with slopes of
0,-3/5,-3/2

That gives us three lines (though we need only two):

y - 5/2 = 0(x+2)
y - 3/2 = -3/5(x+1/2)
y = -3/2 (x+1/2)

These all intersect at

(-13/6,5/2)