Final answer:
The center of the circle is at (-1.5, -6.5), and the radius is √18.5, which is approximately 4.3.
Step-by-step explanation:
To find the center and radius of a circle given the diameter's endpoints, you'll need to split the distance between the two endpoints to find the center, and then calculate the length of the radius using the distance formula. For the endpoints (-5, -4) and (2, -9), you calculate the midpoint (center) by taking the average of the x-coordinates and the y-coordinates: ((-5 + 2) / 2, (-4 + (-9)) / 2) which equals (-1.5, -6.5). This is the center of the circle. The radius can be found by calculating the distance between one endpoint and the center. The formula for distance is √((x2 - x1)² + (y2 - y1)²). Substituting the x and y values of our center and one endpoint, we have √((-5 + 1.5)² + (-4 + 6.5)²), which simplifies to √((-3.5)² + (2.5)²) = √(12.25 + 6.25) = √(18.5), approximately. The exact radius value is √18.5, but in common numerical terms, √18.5 is close to 4.3.