Question

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

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

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