Final answer:
To find the length of the radius of the circle, we first need to find the distance between the two endpoints of the diameter. Then, we divide the diameter by 2 to get the radius. Therefore, the length of the radius of the circle is approximately sqrt(113)/2.
Step-by-step explanation:
To find the length of the radius of the circle, we first need to find the distance between the two endpoints of the diameter. Using the distance formula, we have:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given coordinates, we get:
d = sqrt((-2 - 6)^2 + (-2 - 5)^2)
d = sqrt((-8)^2 + (-7)^2)
d = sqrt(64 + 49)
d = sqrt(113)
Since the diameter is the line segment connecting the two endpoints, the length of the diameter is twice the length of the radius. Therefore, the radius of the circle is half the length of the diameter:
radius = d/2 = sqrt(113)/2
So, the length of the radius of the circle is approximately sqrt(113)/2.