Explain why |−3| + |9| represents the distance between the points (−3Explain why |−3| + |9| represents the distance between the points (−3,

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Explain why |−3| + |9| represents the distance between the points (−3Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5)., −5) and (9, −5).

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Bình An 4 months 2021-07-26T02:09:24+00:00 1 Answers 4 views 0

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    2021-07-26T02:10:32+00:00

    Answer:

    Here we need to use:

    \sqrt{x^2} = |x|

    The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

    D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

    Then the distance between:

    (-3, -5) and (9, -5) is just:

    D = \sqrt{(-3 - 9)^2 - (-5 - (-5))^2} \\\\D = \sqrt{(-3 - 9)^2}  = |-3 - 9|

    because both numbers inside the absolute value, we can rewrite it as:

    |-3 – 9| = |-3| + |-9| = |-3| + |9| = 12

    So, by finding the distance between  (−3, −5) and (9, −5), we got the given expression, in this way we prove that the given expression represents the distance between these points.

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