Question

What is the distance between (-2,-8)(7,-3)

Answer 1

`√(106)` or 10.29563

Explanation:

Use the distance formula to determine the distance between the two points.

`d = \sqrt{(x_(2) -x_(1))^(2) + (y_(2) - x_(1))^(2) }`

d = distance

`(x_(1), y_(1))` = coordinates of the first point

`(x_(2), y_(2))` = coordinates of the second point

Answer 2

`\displaystyle d = √(106)`

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 (-2, -8)

Point (7, -3)

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 = √((7--2)^2+(-3--8)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((9)^2+(5)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(81+25)`
4. [√Radical] Add:
   `\displaystyle d = √(106)`