Question

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

Answer 1

Answer:

$\displaystyle d = \sqrt{65}$

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: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step 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]:                                                        $\displaystyle d = \sqrt{(3-4)^2+(3--5)^2}$
2. [Distance] [√Radical] (Parenthesis) Simplify:                                                 $\displaystyle d = \sqrt{(3-4)^2+(3+5)^2}$
3. [Distance] [√Radical] (Parenthesis) Subtract/Add:                                          $\displaystyle d = \sqrt{(-1)^2+(8)^2}$
4. [Distance] [√Radical] Evaluate exponents:                                                    $\displaystyle d = \sqrt{1+64}$
5. [Distance] [√Radical] Add:                                                                                $\displaystyle d = \sqrt{65}$