Question

-
The distance between (5,6) and (-3.8) is 8.2.
True
False

Answer 1

True

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

Identify

Point (5, 6)

Point (-3, 8)

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 + (8 - 6)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((-8)^2 + (2)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(64 + 4)`
4. [√Radical] Add:
   `\displaystyle d = √(68)`
5. [√Radical] Simplify:
   `\displaystyle d = 2√(17)`
6. Approximate:
   `\displaystyle d \approx 8.24621`