Question

Find the distance between (-5,6)and (3,2).

Answer 1

Answer:

$\displaystyle d = 4\sqrt{5}$

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)

Algebra II

• Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (-5, 6) → x₁ = -5, y₁ = 6

Point (3, 2) → x₂ = 3, y₂ = 2

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

1. Substitute in points [Distance Formulas]:                                                     $\displaystyle d = \sqrt{(3+5)^2+(2-6)^2}$
2. [Distance] [√Radical] (Parenthesis) Add/Subtract:                                       $\displaystyle d = \sqrt{(8)^2+(-4)^2}$
3. [Distance] [√Radical] Evaluate exponents:                                                    $\displaystyle d = \sqrt{64+16}$
4. [Distance] [√Radical] Add:                                                                             $\displaystyle d = \sqrt{80}$
5. [Distance] [√Radical] Simplify:                                                                         $\displaystyle d = 4\sqrt{5}$