Question

what is the radius of this circle?

Explanation:

Step1: Identify center and a point on the circle

The center of the circle is at \((0, 9)\) (wait, looking at the graph, the center is on the y - axis? Wait, no, the y - axis is labeled with 8,9,10? Wait, the grid: let's check the coordinates. The center is at (0,9)? Wait, no, the circle is on the y - axis? Wait, the x - axis and y - axis: the x - axis goes from - 10 to 10, y - axis too. The center of the circle is at (0,9)? Wait, no, the circle is between y = 8 and y = 10. Wait, the center is at (0,9), and the circle goes from y = 8 to y = 10. So the distance from the center (9 on y - axis) to a point on the circle (8 or 10 on y - axis) is \(|10 - 9|=1\) or \(|9 - 8| = 1\). Wait, maybe I misread. Wait, the center is at (0,9)? Wait, no, the blue dot is at (0,9)? Wait, the grid lines: each grid square is 1 unit. So the center is at (0,9), and the circle has a radius that spans 1 unit (from y = 8 to y = 10, so the radius is \(10 - 9=1\) or \(9 - 8 = 1\)). Wait, let's check the horizontal? No, the circle is vertical? Wait, no, the circle is centered at (0,9) and has a radius. Let's see the distance from center to the edge. The center is at (0,9), and the circle reaches to y = 8 and y = 10. So the radius \(r=10 - 9 = 1\) (or \(9 - 8=1\)).

Step2: Calculate the radius

The radius is the distance from the center of the circle to any point on the circle. If the center is at \(y = 9\) and a point on the circle is at \(y = 10\) (or \(y = 8\)), then the radius \(r=\vert10 - 9\vert=1\) (or \(r=\vert9 - 8\vert = 1\)).

Answer:

1