Answer:
(7, 19)
Step-by-step explanation:
We know that we are talking about circle C, which means that the center is point C. Since the diameter is AB, that means that AB goes through the center C and that center C is the midpoint of the segment AB.
Say the coordinates of B are (x, y). We can use the Midpoint Theorem to figure out B. The Midpoint Theorem states that for two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the coordinates of the midpoint are: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex].
Here, our two points are A(5, 1) and B(x, y). Then, the midpoint is: [tex](\frac{5+x}{2} ,\frac{1+y}{2} )[/tex]. We already know the midpoint is C(6, 10), so we can just set 6 equal to [tex]\frac{5+x}{2}[/tex] and set 10 equal to [tex]\frac{1+y}{2}[/tex]:
6 = [tex]\frac{5+x}{2}[/tex] ⇒ 12 = 5 + x ⇒ x = 12 - 5 = 7
AND
10 = [tex]\frac{1+y}{2}[/tex] ⇒ 20 = 1 + y ⇒ y = 20 - 1 = 19
So, the coordinates of B is: (7, 19).
Hope this helps!
