Question

Find the distance between these points in two ways: (-2, 5) and (4, 13).

a. Use the point ( - 2, 5) as (x1, y1) and the point (4, 13) as (x2, y2) in the distance
formula.

Answer 1

`\displaystyle d = 10`

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, 5)

Point (4, 13)

Step 2: Identify

x₁ = -2, y₁ = 5

x₂ = 4, y₂ = 13

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 = √((4+2)^2+(13-5)^2)`
2. [Distance] [√Radical] (Parenthesis) Add/Subtract:
   `\displaystyle d = √((6)^2+(8)^2)`
3. [Distance] [√Radical] Evaluate exponents:
   `\displaystyle d = √(36+64)`
4. [Distance] [√Radical] Add:
   `\displaystyle d = √(100)`
5. [Distance] [√Radical] Evaluate:
   `\displaystyle d = 10`