Question

What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary.

Answer 1

`\displaystyle d = 5.7`

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 (2, 3)

Point (-2, 7)

Step 2: Identify

(2, 3) → x₁ = 2, y₁ = 3

(-2, 7) → x₂ = -2, y₂ = 7

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 = √((-2-2)^2+(7-3)^2)`
2. [Distance] [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((-4)^2+(4)^2)`
3. [Distance] [√Radical] Evaluate exponents:
   `\displaystyle d = √(16+16)`
4. [Distance] [√Radical] Add:
   `\displaystyle d = √(32)`
5. [Distance] [√Radical] Simplify:
   `\displaystyle d = 4√(2)`
6. [Distance] Evaluate:
   `\displaystyle d = 5.65685`
7. [Distance] Round:
   `\displaystyle d = 5.7`