Answer:
B. (-19, 15)
Explanation:
The equation of a circle is generally given as;
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the coordinate of the center of the circle and r is the radius.
Given the point (-18, 15) and radius of 1, our equation of a circle will become;
[tex](-18-h)^2_{}+(15-k)^2=1\ldots\ldots...\ldots\ldots\ldots\ldots\text{.Equation 1}[/tex]Given the point (-20, 15), our equation of a circle will become;
[tex](-20-h)^2+(15-k)^2=1\ldots\ldots\ldots\ldots\ldots..Equation\text{ 2}[/tex]Let's go ahead and subtract Equation 2 from Equation 1, we'll have;
[tex]\begin{gathered} (-18-h)^2-(-20-h)^2+0=0 \\ 324+36h+h^2-400-40h-h^2=0 \\ -76-4h=0 \\ h=-\frac{76}{4} \\ h=-19 \end{gathered}[/tex]Let's substitute h with -19 in Equation 1 and solve for k;
[tex]\begin{gathered} (-18+19)^2+(15-k)^2=1 \\ 1+(15-k)^2=1 \\ (15-k)^2=0 \\ 15-k=0 \\ -k=-15 \\ k=15 \end{gathered}[/tex]Therefore, the coordinates of the center of the circle is (-19, 15)
