Question

What is the distance between the points M(–21, –7) and N(–5, –7)?

Answer 1

`\displaystyle d = 16`

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 M(-21, -7)

Point N(-5, -7)

Step 2: Identify

M(-21, -7) → x₁ = -21, y₁ = -7

N(-5, -7) → x₂ = -5, y₂ = -7

Step 3: 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+21)^2+(-7+7)^2)`
2. [Distance] [√Radical] (Parenthesis) Add:
   `\displaystyle d = √((16)^2+(0)^2)`
3. [Distance] [√Radical] Evaluate exponent:
   `\displaystyle d = √((16)^2)`
4. [Distance] Evaluate radical:
   `\displaystyle d = 16`