To determine which point represents the center of the circle given by the equation [tex]\((x - 3)^2 + (y - 2)^2 = 16\)[/tex], we need to recall the general form of the equation of a circle. The general form is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
Here, [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
Given the equation [tex]\((x - 3)^2 + (y - 2)^2 = 16\)[/tex], we can see that this matches the general form of a circle's equation, with [tex]\(h\)[/tex] and [tex]\(k\)[/tex] being the coordinates of the center.
By comparing the given equation to the general form, we identify:
- [tex]\(h = 3\)[/tex]
- [tex]\(k = 2\)[/tex]
- [tex]\(r^2 = 16\)[/tex] (though the radius is irrelevant for finding the center)
Thus, the center of the circle is [tex]\((h, k)\)[/tex], which is [tex]\((3, 2)\)[/tex].
Therefore, the point that represents the center of the circle is:
[tex]\[ \boxed{(3, 2)} \][/tex]
By carefully analyzing the options provided:
- [tex]\(A. (-3, 2)\)[/tex]
- [tex]\(B. (3, -2)\)[/tex]
- [tex]\(C. (-3, -2)\)[/tex]
- [tex]\(D. (3, 2)\)[/tex]
It is clear that the correct answer is:
[tex]\[ \boxed{(3, 2)} \][/tex]
