Question

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

Answer 1

`\displaystyle d = 4√(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 = √((x_2-x_1)^2+(y_2-y_1)^2)`

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 = √((3+5)^2+(2-6)^2)`
2. [Distance] [√Radical] (Parenthesis) Add/Subtract:
   `\displaystyle d = √((8)^2+(-4)^2)`
3. [Distance] [√Radical] Evaluate exponents:
   `\displaystyle d = √(64+16)`
4. [Distance] [√Radical] Add:
   `\displaystyle d = √(80)`
5. [Distance] [√Radical] Simplify:
   `\displaystyle d = 4√(5)`