Final answer:
To find the center and radius of a circle given two endpoints, use the midpoint formula to find the center and the distance formula to find the radius.
Step-by-step explanation:
To find the center and radius of a circle given two endpoints, you can use the midpoint formula and the distance formula.
First, use the midpoint formula to find the coordinates of the center of the circle. The midpoint formula is:
Midpoint = ((x_1 + x_2)/2, (y_1 + y_2)/2)
In this case, the coordinates of the endpoints are (-9,2) and (15,12), so the midpoint would be ((-9+15)/2, (2+12)/2) = (3,7).
Next, use the distance formula to find the radius of the circle. The distance formula is:
Distance = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)
In this case, the coordinates of the endpoints are (-9,2) and (15,12), so the distance would be sqrt((15-(-9))^2 + (12-2)^2) = sqrt(24^2 + 10^2) = sqrt(576 + 100) = sqrt(676) = 26.
Therefore, the center of the circle is (3,7) and the radius is 26.