To determine the length of segment [tex]\( KL \)[/tex], which is the diameter of the circle represented by the equation [tex]\((x - 11)^2 + (y + 15)^2 = 7\)[/tex], we need to interpret this equation in terms of its standard form.
The standard form of a circle's equation is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
From the equation [tex]\((x - 11)^2 + (y + 15)^2 = 7\)[/tex], we can observe the following:
- The center of the circle [tex]\((h, k)\)[/tex] is [tex]\((11, -15)\)[/tex].
- The radius squared [tex]\(r^2\)[/tex] is [tex]\(7\)[/tex].
To find the radius [tex]\(r\)[/tex] of the circle, we take the square root of [tex]\(7\)[/tex]:
[tex]\[
r = \sqrt{7}
\][/tex]
The diameter [tex]\(KL\)[/tex] of the circle is twice the radius:
[tex]\[
KL = 2 \times r = 2 \times \sqrt{7}
\][/tex]
Thus, [tex]\(KL = 2 \sqrt{7}\)[/tex].
So, the correct answer is:
C. [tex]\(2 \sqrt{7}\)[/tex]
