Question

The center of circle Z has coordinates (0, 2). If circle Z passes through R(3, -1), what is the length of its diameter?

Answer 1

The diameter of circle Z is 6sqrt(2).

Step-by-step explanation:

The distance between the center of the circle and a point on its circumference is called the radius. Given that the center of circle Z has coordinates (0, 2) and it passes through point R(3, -1), we can calculate the distance between these two points to find the radius. Using the distance formula, we have:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

1. Distance = sqrt((3 - 0)^2 + (-1 - 2)^2)

2. Distance = sqrt(9 + 9)

3. Distance = sqrt(18)

4. Distance = 3sqrt(2)

The diameter of a circle is twice its radius. Therefore, the diameter of circle Z is 2 * 3sqrt(2), which simplifies to 6sqrt(2)