Question

Find the distance d(P1, P2) between the points P1 and P2.

P1 = (4,-5); P2 = (3,3)

d(P1,P2) =
(Simplify your answer. Type an exact answer, using radicals as needed.)

Answer 1

`\displaystyle d = √(65)`

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

P1 (4, -5) → x₁ = 4, y₁ = -5

P2 (3, 3) → x₂ = 3, y₂ = 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 = √((3-4)^2+(3--5)^2)`
2. [Distance] [√Radical] (Parenthesis) Simplify:
   `\displaystyle d = √((3-4)^2+(3+5)^2)`
3. [Distance] [√Radical] (Parenthesis) Subtract/Add:
   `\displaystyle d = √((-1)^2+(8)^2)`
4. [Distance] [√Radical] Evaluate exponents:
   `\displaystyle d = √(1+64)`
5. [Distance] [√Radical] Add:
   `\displaystyle d = √(65)`