Question

Calculate the distance between the points M=(-2, 1) and K=(2, -4) in the coordinate plane.

Answer 1

`\displaystyle d = √(41)`

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 M(-2, 1)

Point K(2, -4)

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 = √((2+2)^2+(-4-1)^2)`
2. [Distance] [√Radical] (Parenthesis) Add/Subtract:
   `\displaystyle d = √((4)^2+(-5)^2)`
3. [Distance] [√Radical] Evaluate exponents:
   `\displaystyle d = √(16+25)`
4. [Distance] [√Radical] Add:
   `\displaystyle d = √(41)`