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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.)

Respuesta :

Space

Answer:

[tex]\displaystyle d = \sqrt{65}[/tex]

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: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

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

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