Question

what is the radius of this circle?

Explanation:

Step1: Identify the center and a point on the circle

The center of the circle is at the origin \((0,0)\) (the intersection of the x - and y - axes). A point on the circle can be seen by looking at the grid. For example, the rightmost point of the circle is at \((1,0)\) (since from the center \((0,0)\) to \((1,0)\) is along the x - axis).

Step2: Calculate the distance from the center to the point (radius)

The radius \(r\) of a circle is the distance from the center \((x_1,y_1)\) to a point \((x_2,y_2)\) on the circle, given by the distance formula \(r=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1 = 0,x_2=1,y_2 = 0\). So \(r=\sqrt{(1 - 0)^2+(0 - 0)^2}=\sqrt{1+0}=1\). Alternatively, by looking at the grid, since each grid square has a side length of 1 unit, and the circle extends from \(x=- 1\) to \(x = 1\) (or \(y=-1\) to \(y = 1\)) from the center, the radius is 1 unit.

Answer:

1