Question

Find the distance between the points (4,-8) and (7-10).

Answer 1

The distance between the points (4,-8) and (7-10)

`= \sqrt{ {(7 - 4)}^(2) + {( - 10 - ( - 8))}^(2) } \\ = \sqrt{ {(7 - 4)}^(2) + {( - 10 + 8)}^(2) } \\ = \sqrt{ {3}^(2) + { (- 2)}^(2) } \\ = √(9 + 4) \\ = √(13) \: units`

√13 is the right answer.

Answer 2

`\displaystyle d = √(13)`

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 (4, -8)

Point (7, -10)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

1. Substitute in points [DF]:
   `\displaystyle d = √((7-4)^2+(-10+8)^2)`
2. (Parenthesis) Subtract/Add:
   `\displaystyle d = √((3)^2+(-2)^2)`
3. [√Radical] Exponents:
   `\displaystyle d = √(9+4)`
4. [√Radical] Add:
   `\displaystyle d = √(13)`