Question

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

Answer 1

Answer:

$\displaystyle d = 2\sqrt{13}$

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

Step-by-step 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]:                                                       $\displaystyle d = \sqrt{(5-11)^2+(8-4)^2}$
2. [√Radical] (Parenthesis) Subtract:                                                                 $\displaystyle d = \sqrt{(-6)^2+(4)^2}$
3. [√Radical] Evaluate exponents:                                                                    $\displaystyle d = \sqrt{36+16}$
4. [√Radical] Add:                                                                                               $\displaystyle d = \sqrt{52}$
5. [√Radical] Simplify:                                                                                         $\displaystyle d = 2\sqrt{13}$