Final answer:
The length of the radius of the circle is approximately 4.91.
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 (-5,2) and (4,4) which is the diameter of the circle. We can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values, we get:
d = sqrt((4 - -5)^2 + (4 - 2)^2) = sqrt(9^2 + 2^2) = sqrt(81 + 4) = sqrt(85)
Since the diameter is twice the length of the radius, we can divide the distance by 2 to find the radius:
radius = sqrt(85) / 2 ≈ 4.91
Therefore, the length of the radius of the circle is approximately 4.91.