Answer:
The center of the circle is [tex]C(x,y) = (2, 3)[/tex].
Step-by-step explanation:
The center of the circle is the midpoint of the segment between the endpoints. We can determine the location of the center by this vectorial expression:
[tex]C(x,y) = \frac{1}{2}\cdot R_{1}(x,y)+ \frac{1}{2}\cdot R_{2}(x,y)[/tex] (1)
Where:
[tex]C(x,y)[/tex] - Center.
[tex]R_{1} (x,y)[/tex], [tex]R_{2} (x,y)[/tex] - Location of the endpoints.
If we know that [tex]R_{1} (x,y) = (-2,10)[/tex] and [tex]R_{2} (x,y) = (6,-4)[/tex], then the location of the center of the circle is:
[tex]C(x,y) = \frac{1}{2}\cdot (-2,10)+\frac{1}{2}\cdot (6,-4)[/tex]
[tex]C(x,y) = (-1, 5) + (3, -2)[/tex]
[tex]C(x,y) = (2, 3)[/tex]
The center of the circle is [tex]C(x,y) = (2, 3)[/tex].
