Final answer:
The radius of the circle with a diameter AB located at (-8,-8) and (2,2) is 5√2, calculated using the distance formula followed by dividing the diameter by 2.
Step-by-step explanation:
To find the radius of the circle given the coordinates of the diameter AB at (-8,-8) and (2,2), we first need to calculate the distance between these two points. This distance represents the diameter of the circle. We can use the distance formula, which is the square root of the sum of the squares of the differences in x-coordinates and y-coordinates:
Distance AB = √ [ (x2 - x1)^2 + (y2 - y1)^2 ]
Substituting the coordinates into the formula, we get:
Distance AB = √ [ (2 - (-8))^2 + (2 - (-8))^2 ]
Distance AB = √ [ (10)^2 + (10)^2 ]
Distance AB = √ [ 100 + 100 ]
Distance AB = √ 200
Distance AB = 10√2
Since the diameter of the circle is 10√2, we divide by 2 to find the radius:
Radius = (10√2) / 2
Radius = 5√2
Therefore, the radius of the circle is 5√2.