Find the radius of the circle. The center of the circle is (2, -3) and a point that lies on the circle is (-1, -2).

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Geometry

Definition of a radius - the center of a circle to any point to the circumference

Algebra II

Distance Formula:

Step-by-step explanation:

Step 1: Define

Center (2, -3) → x₁ = 2, y₁ = -3

Circumference point (-1, -2) → x₂ = -1, y₂ = -2

In this case, the distance d from the center to the circumference point would be the radius r of the circle.

Step 2: Find Radius r

[Distance Formula] Define equation [Radius]:                                               Substitute in points [Radius]:                                                                         [Radius] [√Radical] (Parenthesis) Simplify:                                                     [Radius] [√Radical] (Parenthesis) Subtract/Add:                                           [Radius] [√Radical] Evaluate exponents:                                                       [Radius] [√Radical] Add: