Question

what is the diameter of this circle?
(grid with a circle centered at the origin (0,0), intersecting the x - axis at (-4,0) and (4,0), and the y - axis at (0, - 4) and (0,4))
submit button and work it out text

Explanation:

Step1: Identify the radius

The center of the circle is at the origin \((0,0)\). The circle intersects the x - axis at \(x = 4\) and \(x=- 4\). The distance from the center \((0,0)\) to a point on the circle (e.g., \((4,0)\)) is the radius \(r\). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \((0,0)\) and \((4,0)\), we have \(r=\sqrt{(4 - 0)^2+(0 - 0)^2}=4\).

Step2: Calculate the diameter

The formula for the diameter \(d\) of a circle is \(d = 2r\). Since \(r = 4\), then \(d=2\times4 = 8\).

Answer:

8