Question

Find the distance between the two points rounding to the nearest tenth (if necessary).

(-6, 6) and (3, -6)

Answer 1

`\displaystyle d = 15`

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 (-6, 6)

Point (3, -6)

Step 2: Identify

(-6, 6) → x₁ = -6, y₁ = 6

(3, -6) → x₂ = 3, y₂ = -6

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 = √((3--6)^2+(-6-6)^2)`
2. [√Radical] (Parenthesis) Subtract/Add:
   `\displaystyle d = √((9)^2+(-12)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(81+144)`
4. [√Radical] Add:
   `\displaystyle d = √(225)`
5. [√Radical] Evaluate:
   `\displaystyle d = 15`