Question

what is the diameter of this circle?

Explanation:

Step1: Identify the radius

The center of the circle is at \((-1, 0)\) (from the green dot) and a point on the circle is at \((8, 0)\) (where the circle intersects the x - axis on the right) or \((-10, 0)\) (where it intersects on the left). Let's use the right - most point \((8,0)\) and the center \((-1,0)\). The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Since \(y_1 = y_2=0\), the distance (radius \(r\)) is \(|8-(-1)|=|8 + 1| = 9\)? Wait, no, wait. Wait, looking at the grid, the center is at \((-1,0)\)? Wait, no, maybe I misread the center. Wait, the green dot is at \((-1,0)\)? Wait, no, the grid lines: each grid square is 1 unit. Wait, the center is at \((-1,0)\)? Wait, no, let's check the left - most point: the circle intersects the x - axis at \(x=-10\) and \(x = 8\)? Wait, no, wait the left - most point is at \(x=-10\) (since the arrow is at - 10) and the right - most point is at \(x = 8\)? Wait, no, that can't be. Wait, maybe the center is at \((-1,0)\), and the right - most point is at \(x = 8\), so the distance from center \((-1,0)\) to \((8,0)\) is \(8-(-1)=9\), and the left - most point is at \(x=-10\), distance from center \((-1,0)\) to \((-10,0)\) is \(\vert-1-(-10)\vert=\vert9\vert = 9\). Wait, but the diameter is the distance between the left - most and right - most points. The left - most point is at \(x=-10\) (y = 0) and the right - most point is at \(x = 8\) (y = 0). The distance between \((-10,0)\) and \((8,0)\) is \(8-(-10)=18\)? Wait, no, wait, maybe I made a mistake. Wait, looking at the grid, the center is at \((-1,0)\)? Wait, no, maybe the center is at \((-1,0)\), and the radius is 9, so diameter is \(2\times9 = 18\)? Wait, no, wait the left - most point: let's count the grid squares. From \(x=-10\) to \(x = 8\), the number of units is \(8-(-10)=18\). So the diameter is the distance between the two points on the circle along the x - axis (since they are on the same horizontal line, the diameter is the horizontal distance between them).

Step2: Calculate the diameter

The left - most point of the circle on the x - axis is at \(x=-10\) and the right - most point is at \(x = 8\). The distance between these two points is \(d=\vert8-(-10)\vert=\vert8 + 10\vert=18\). Alternatively, since the radius is the distance from the center to a point on the circle. If the center is at \((-1,0)\), and the right - most point is at \((8,0)\), the radius \(r=8-(-1)=9\), so the diameter \(d = 2r=2\times9 = 18\).

Answer:

18