Final answer:
To find the radius of the circle, we use the distance formula to calculate the length of the diameter given by the endpoints (-4,-2) and (8,3), which is 13 units. Dividing the diameter by 2 gives us the radius, which is 6.5 units.
Step-by-step explanation:
The question asks us to find the radius of the circle given the endpoints of its diameter. The endpoints of the diameter are (-4,-2) and (8,3). Using the distance formula, we can find the diameter of the circle. The distance formula is:
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
Which gives us:
d = \sqrt{(8 - (-4))^2 + (3 - (-2))^2} = \sqrt{(12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13
Since the diameter (d) is 13, we divide it by 2 to find the radius (r):
r = d/2 = 13/2 = 6.5
Therefore, the radius of the circle is 6.5 units.