Question

What is the distance between the points (2, 1) and(6, 7)?

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

Identify

Point (2, 1)

Point (6, 7)

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 = √((6 - 2)^2 + (7 - 1)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √(4^2 + 6^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(16 + 36)`
4. [√Radical] Add:
   `\displaystyle d = √(52)`
5. [√Radical] Simplify:
   `\displaystyle d = 2√(13)`