Question

find the coordinate of the circumcenter ABC with vertices A (0,0) B (3,0) C (3,2)

Answer 1

@Will.H

Answer 2

A (0,0)
B (1.5,1)
C (2.5,1.5)
D (6,2)

Answer 3

@563blackghost can u help

Answer 4

The circumcenter is the center of the circle passing through the given vertices.

Consider the general equation for a circle centered at \((a,b)\) with radius \(r\):
\[(x-a)^2+(y-b)^2=r^2\]If you plug in each vertex's coordinate for \((x,y)\) in the above equation, you end up with the system
\[\begin{cases}
a^2+b^2=r^2&\text{when }(x,y)=(0,0)\\[1ex]
(a-3)^2+b^2=r^2&\text{when }(x,y)=(3,0)\\[1ex]
(a-3)^2+(b-2)^2=r^2&\text{when }(x,y)=(3,2)
\end{cases}\]which can be solved for \(a,b,r\), but you only need the first two to find the center.

Answer 5

so would the answer be A (0,0)

Answer 6

Have you tried solving the system? I'm not here to hand out answers.