Answer:
A(-6, -5)
Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center at (-2, -2) → h = -2, k = -2,
and the diameter d = 2r = 10 → r = 5.
Substitute:
[tex](x-(-2))^2+(y-y(-2))^2=5^2\\\\(x+2)^2+(y+2)^2=25[/tex]
We have two ways to the solution of this question.
I. Calculate the distance between the center and the given points using formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
If the distance d is equal to the radius, then the point lies on a circle.
II. Put the coordinates of the given points to the equation and check the equality.
I'll use first way for the points A and B, and second way for the points C and D.
[tex]A(-6,\ -5),\ O(-2,\ -2)\\\\d=\sqrt{(-2-(-6))^2+(-2-(-5))^2}=\sqrt{(-2+6)^2+(-2+5)^2}\\\\=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5=r\\\\\bold{CORRECT\ :)}\\\\B(-2,\ -2)\\\\\text{I will not check it because it is the center of the circle.}\\\text{The center of the circle does not belong to the circle.}[/tex]
[tex]C(6,\ 4),\ (x+2)^2+(y+2)^2=25\\\\(6+2)^2+(4+2)^2=8^2+6^2=64+36=100\neq25\\\\\bold{INCORRECT\ :(}\\\\D(8,\ 8),\ (x+2)^2+(y+2)^2=25\\\\(8+2)^2+(8+2)^2=10^2+10^2=100+100=200\neq25\\\\\bold{INCORRECT\ :(}[/tex]
