Final answer:
The center of the circle is (-1.5, -2) and the radius is 3.205.
Step-by-step explanation:
To find the center and radius of the circle, we can use the formula for the distance between two points in a coordinate plane. The two points given are (-3, -4) and the origin (0, 0), which represents the diameter of the circle. The center of the circle is the midpoint of the diameter, which can be found by taking the average of the x-coordinates and the y-coordinates. So, the center is ( (-3+0)/2 , (-4+0)/2 ) = (-1.5, -2). The radius of the circle is half the length of the diameter, which can be found using the distance formula as the distance between the center and one of the endpoints of the diameter. So, the radius is the distance between (-1.5, -2) and (-3, -4), which is √((-3-(-1.5))² + (-4-(-2))²) = √(2.5² + 2²) = √(6.25 + 4) = √10.25 = 3.205.