Question

what is the radius of this circle?

Explanation:

Step1: Observe the circle on the grid

The circle is centered at (-6, 6) (from the grid coordinates). To find the radius, we can look at the horizontal or vertical distance from the center to the edge of the circle.

Step2: Calculate the radius

Looking at the x - coordinates (or y - coordinates) of the center and the edge of the circle. The center is at x = - 6, and the rightmost point of the circle is at x=-5 (or leftmost at x = - 7), the distance between - 6 and - 5 (or - 6 and - 7) is 1 unit? Wait, no, wait. Wait, looking at the grid, the circle's diameter: from the left side of the circle to the right side. Let's count the grid squares. The center is at (-6,6). The circle extends from, say, x=-7 to x=-5 (since the center is at x=-6). The distance from -6 to -5 is 1, and from -6 to -7 is also 1. Wait, no, maybe I miscounted. Wait, the circle's radius: let's see the grid lines. Each grid square is 1 unit. The circle has a diameter of 2 units (from x=-7 to x=-5, which is 2 units), so the radius is half of the diameter. So diameter $d = 2$ (since from -7 to -5 is 2 units), so radius $r=\frac{d}{2}=\frac{2}{2} = 1$? Wait, no, wait. Wait, the center is at (-6,6). Let's check the horizontal direction: the circle's leftmost point is at x=-7 and rightmost at x=-5. The distance between -7 and -5 is $|-5-(-7)|=2$ units, so diameter is 2, radius is 1. Alternatively, vertical direction: center at y = 6, top at y = 7, bottom at y = 5. Distance between 5 and 7 is 2, so diameter 2, radius 1. Wait, but maybe I made a mistake. Wait, looking at the circle, the center is at (-6,6). The circle's radius: from center to edge. Let's count the grid squares. From (-6,6) to (-5,6) is 1 unit (right), to (-7,6) is 1 unit (left), to (-6,7) is 1 unit (up), to (-6,5) is 1 unit (down). So the radius is 1 unit? Wait, no, maybe the circle has a radius of 1? Wait, but let's check again. Wait, the circle is drawn with center at (-6,6), and the circle's radius: the distance from center to the circumference. So if from (-6,6) to (-5,6) is 1, then radius is 1. Wait, but maybe the grid is such that each square is 1 unit, so the radius is 1. Wait, but maybe I misread. Wait, the circle: let's see the coordinates. The center is at (-6,6). The circle's rightmost point is at x=-5 (so x - coordinate of center is -6, rightmost is -5, so distance is $|-5 - (-6)|=1$). Similarly, leftmost is -7, distance $|-7-(-6)| = 1$. Top is y = 7, distance $|7 - 6|=1$, bottom is y = 5, distance $|5 - 6|=1$. So the radius is 1. Wait, but maybe the circle is larger? Wait, no, the circle in the image: looking at the grid, the circle has a diameter of 2 units (since from -7 to -5 is 2 units), so radius is 1.

Wait, maybe I made a mistake. Wait, let's check the grid again. The x - axis: from -10 to 10, each grid line is 1 unit. The center is at (-6,6). The circle: the left side is at x=-7, right side at x=-5. So the length from -7 to -5 is 2 units (diameter), so radius is 1. So the radius is 1.

Answer:

1