Question

what is the diameter of this circle?
(graph with x-axis from -10 to 10, y-axis from -10 to 10, circle centered at (8,0))

Explanation:

Step1: Determine the radius from the graph

Looking at the circle centered at \( x = 8 \) on the coordinate grid, we can see that the circle spans 1 unit to the left and 1 unit to the right of the center (since it fits within the grid squares). So the radius \( r \) is 1 unit? Wait, no, wait. Wait, looking at the grid, each square is 1 unit. Wait, the circle is from, let's see, the center is at (8,0). The leftmost point of the circle is at x=7, and the rightmost at x=9? Wait, no, wait the circle is drawn with center at (8,0), and the diameter: let's count the grid squares. From x=7 to x=9? Wait, no, maybe I miscounted. Wait, the circle's diameter: looking at the graph, the circle is 2 units wide? Wait, no, wait each grid line is 1 unit. Let's check the horizontal length. The center is at x=8. The left side of the circle is at x=7 (8 - 1) and the right side at x=9 (8 + 1)? No, that would be radius 1, diameter 2. Wait, but maybe the circle is from x=7 to x=9, so the distance between 7 and 9 is 2 units. Wait, but maybe I made a mistake. Wait, let's look again. The circle is centered at (8,0), and the diameter: the horizontal extent. From x=7 to x=9, so the length is 9 - 7 = 2? Wait, no, that can't be. Wait, maybe the circle is 2 units in diameter? Wait, no, maybe each square is 1 unit, so the diameter is 2 units? Wait, no, maybe I'm wrong. Wait, let's count the number of grid squares. The center is at (8,0). The leftmost point is at x=7 (8 - 1) and rightmost at x=9 (8 + 1), so the distance between 7 and 9 is 2, so diameter is 2? Wait, but maybe the circle is 2 units. Wait, but let's confirm. The diameter is twice the radius. If the radius is 1 (from center 8 to 7 or 9), then diameter is 21=2. Wait, but maybe the circle is 2 units in diameter. Wait, but let's check the graph again. The circle is drawn with center at (8,0), and the horizontal length: from x=7 to x=9, so 2 units. So diameter is 2. Wait, but maybe I miscounted. Wait, the grid lines: from x=7 to x=9, that's 2 units. So the diameter is 2. Wait, but maybe the answer is 2? Wait, no, wait maybe the circle is 2 units? Wait, let's see. Each grid square is 1 unit. So the diameter is 2 units. Wait, but maybe I made a mistake. Wait, let's calculate the distance between the left and right endpoints. The left endpoint is at x=7, right at x=9. So 9 - 7 = 2. So diameter is 2. Wait, but maybe the circle is 2 units. So the diameter is 2. Wait, but let's check again. The center is at (8,0). The radius is the distance from center to edge. From (8,0) to (7,0) is 1 unit, so radius is 1. Then diameter is 21=2. So the diameter is 2. Wait, but maybe the answer is 2. Wait, but let's confirm. So step 1: find the radius by looking at the grid. The center is at (8,0), and the edge is at (7,0) or (9,0), so radius is 1. Step 2: diameter is 2radius = 21 = 2. So the diameter is 2.

Step1: Identify the radius from the graph

The circle is centered at \((8, 0)\) on the coordinate grid. The leftmost point of the circle is at \(x = 7\) (1 unit left of the center), and the rightmost at \(x = 9\) (1 unit right of the center). Thus, the radius \(r = 1\) unit.

Step2: Calculate the diameter

The formula for the diameter \(d\) of a circle is \(d = 2r\). Substituting \(r = 1\), we get \(d = 2 \times 1 = 2\).

Answer:

2