Question

Which expression represents the distance between the points (11, 4) and (5,8)?

Answer 1

`\displaystyle d = 2√(13)`

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 (11, 4) → x₁ = 11, y₁ = 4

Point (5, 8) → x₂ = 5, y₂ = 8

Step 2: Find distance d

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

1. Substitute in points [Distance Formula]:
   `\displaystyle d = √((5-11)^2+(8-4)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((-6)^2+(4)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(36+16)`
4. [√Radical] Add:
   `\displaystyle d = √(52)`
5. [√Radical] Simplify:
   `\displaystyle d = 2√(13)`