Question

the points (-9, -3) and (8,8) are the endpoints of the diameter of a circle. find the length of the radius of the circle. (round to the nearest hundredth as needed ) the length of the radius is 10.13

Explanation:

Step1: Find the length of the diameter using the distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \((x_1, y_1)=(-9, -3)\) and \((x_2, y_2)=(8, 8)\).
So, \(d=\sqrt{(8 - (-9))^2+(8 - (-3))^2}=\sqrt{(17)^2+(11)^2}=\sqrt{289 + 121}=\sqrt{410}\approx20.25\)

Step2: Find the radius (radius is half of the diameter)

Radius \(r=\frac{d}{2}\), so \(r = \frac{\sqrt{410}}{2}\approx\frac{20.25}{2}=10.125\approx10.13\)

Answer:

The length of the radius is approximately \(\boldsymbol{10.13}\)