Question

Find the distance between the

following points using the
Pythagorean theorem: (5, 10)
and (10, 12)

Answer 1

`\displaystyle d = √(29)`

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:

*Note:

The distance formula is derived from the Pythagorean Theorem.

Step 1: Define

Identify

Point (5, 10)

Point (10, 12)

Step 2: Find distance d

1. Substitute in points [Distance Formula]:
   `\displaystyle d = √((10 - 5)^2 + (12 -10)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √(5^2 + 2^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(25 + 4)`
4. [√Radical] Add:
   `\displaystyle d = √(29)`