Question

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).

Answer 1

Answer:

$\displaystyle r = \sqrt{10}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. 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: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

1. [Distance Formula] Define equation [Radius]:                                               $\displaystyle r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
2. Substitute in points [Radius]:                                                                         $\displaystyle r = \sqrt{(-1-2)^2+(-2--3)^2}$
3. [Radius] [√Radical] (Parenthesis) Simplify:                                                     $\displaystyle r = \sqrt{(-1-2)^2+(-2+3)^2}$
4. [Radius] [√Radical] (Parenthesis) Subtract/Add:                                           $\displaystyle r = \sqrt{(-3)^2+(1)^2}$
5. [Radius] [√Radical] Evaluate exponents:                                                       $\displaystyle r = \sqrt{9+1}$
6. [Radius] [√Radical] Add:                                                                                 $\displaystyle r = \sqrt{10}$