Final answer:
The radius of the circle, whose diameter endpoints are (-1,-4) and (7, 7), is half the distance between these two points, which is calculated using the distance formula. The result is that the radius is the square root of 185, divided by 2.
Step-by-step explanation:
To find the length of the radius of a circle with endpoints of the diameter at (-1,-4) and (7, 7), we need to first calculate the length of the diameter using the distance formula.
The distance formula is
d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1,y1) and (x2,y2) are the coordinates of the two points.
Using the given points (-1,-4) (x1,y1) and (7, 7) (x2,y2):
d = √((7 - (-1))^2 + (7 - (-4))^2) = √((8)^2 + (11)^2) = √(64 + 121) = √185
The diameter is the distance between these two points, which we found to be √185. Therefore, the radius is half of the diameter.
Radius (r) = Diameter (D) / 2
= (√185) / 2
This gives us the radius of the circle.