Question

Find the distance between the points (5,-6), (-3,12)

Answer 1

`\displaystyle d = 2√(97)`

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 (5, -6)

Point (-3, 12)

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 = √((-3-5)^2+(12+6)^2)`
2. [√Radical] (Parenthesis) Subtract/Add:
   `\displaystyle d = √((-8)^2+(18)^2)`
3. [√Radical] Evaluate Exponents:
   `\displaystyle d = √(64+324)`
4. [√Radical] Add:
   `\displaystyle d = √(388)`
5. [√Radical] Simplify:
   `\displaystyle d = 2√(97)`