Cakeislifelol
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What are the coordinates of the circumcenter of a triangle with vertices A(−3,−4), B(1,−4), and C(−3,0)?

Verified Answer :

aclay1026

the coordinate of the circumecenter of a triangle is A

wizard123

The circumcenter is equal distance from all 3 verices.
Using distance formula, equate distance to A with distance to C:
\((x+3)^2 +(y+4)^2 = (x+3)^2 + y^2\)
The x terms cancel, Expand and solve for y:
\(y^2 +8y+16 = y^2\)
\(y = -2\)
Now do same thing for point A and B:
\((x+3)^2 + (y+4)^2 = (x-1)^2 + (y+4)^2\)
y terms cancel
\(x^2 +6x+9 = x^2-2x+1\)
\(x = -1\)

Circumcenter is the point (-1,-2)

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