Question

what is the radius of this circle? (image of a coordinate grid with a circle centered at the origin (0,0) with horizontal and vertical grid lines from -10 to 10)

Explanation:

Step1: Identify the center

The center of the circle is at the origin \((0,0)\) (where the x and y axes intersect).

Step2: Find the distance from center to a point on the circle

Take a point on the circle, for example, \((2,0)\) (or \((0,2)\), \((-2,0)\), \((0,-2)\)). The distance from \((0,0)\) to \((2,0)\) is calculated using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \(x_1 = 0\), \(y_1 = 0\), \(x_2 = 2\), \(y_2 = 0\), so \(d=\sqrt{(2 - 0)^2+(0 - 0)^2}=\sqrt{4}=2\). This distance is the radius.

Answer:

2