Answer:
Option A) Inside the circle
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The radius is equal to the distance from the center to any point on the circle
the formula to calculate the distance between two points is equal to
[tex]d\sqrt{(y2-y1)^2+(x2-x1)^2 }[/tex]
we have
A(-5,-8),M(-1,-3)
substitute the values
[tex]r=\sqrt{(-3+8)^{2}+(-1+5)^{2}}[/tex]
[tex]r=\sqrt{(5)^{2}+(4)^{2}}[/tex]
[tex]r=\sqrt{41}\ units[/tex]
step 2
Find the distance from the center to point V
we know that
If the distance from the center to point V is equal to the radius, then the point V lie on the circle
If the distance from the center to point V is less than the radius, then the point V lie inside the circle
If the distance from the center to point V is greater than the radius, then the point V lie outside the circle
we have
A(-5,-8),V(-11,-6)
substitute in the formula
[tex]d=\sqrt{(-6+8)^{2}+(-11+5)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(-6)^{2}}[/tex]
[tex]d=\sqrt{40}\ units[/tex]
so
[tex]\sqrt{40}\ units< \sqrt{41}\ units[/tex]
The distance from the center to point V is less than the radius
therefore
The point V lie inside the circle
Hope that helped :)
