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What is the approximate distance between points A and B?

A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair 1, 4 is labeled as A, and the ordered pair negative 2, negative 3 is labeled as B.

a. 6.32
b. 6.95
c. 7.62
d. 8.56

What is the approximate distance between points A and B A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1 The ordered pair 1 class=
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Answer:

[tex]\displaystyle d \approx 7.62[/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 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

Find points from graph.

Point A(1, 4)

Point B(-2, -3)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

  1. Substitute in points [DF]:                    [tex]\displaystyle d = \sqrt{(-2-1)^2+(-3-4)^2}[/tex]
  2. (Parenthesis) Subtract:                       [tex]\displaystyle d = \sqrt{(-3)^2+(-7)^2}[/tex]
  3. [√Radical] Exponents:                        [tex]\displaystyle d = \sqrt{9+49}[/tex]
  4. [√Radical] Add:                                   [tex]\displaystyle d = \sqrt{58}[/tex]
  5. [√Radical] Evaluate:                           [tex]d = 7.61577[/tex]
  6. Round:                                                 [tex]\displaystyle d \approx 7.62[/tex]

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