Which expression represents the distance between the points (11, 4) and (5,8)?

Question

Which expression represents the distance between the points (11, 4) and (5,8)?

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Ngọc Hoa 4 weeks 2021-08-17T12:20:24+00:00 1 Answers 2 views 0

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    2021-08-17T12:21:55+00:00

    Answer:

    \displaystyle d = 2\sqrt{13}

    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

    Point (11, 4) → x₁ = 11, y₁ = 4

    Point (5, 8) → x₂ = 5, y₂ = 8

    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{(5-11)^2+(8-4)^2}
    2. [√Radical] (Parenthesis) Subtract:                                                                 \displaystyle d = \sqrt{(-6)^2+(4)^2}
    3. [√Radical] Evaluate exponents:                                                                    \displaystyle d = \sqrt{36+16}
    4. [√Radical] Add:                                                                                               \displaystyle d = \sqrt{52}
    5. [√Radical] Simplify:                                                                                         \displaystyle d = 2\sqrt{13}

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