Mathematics

Question

A student wants to find point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4. Point A is at -6 and point B is at 2. The student's work is shown .

2 Answer

  • Answer:

    Point C at (-18/7)

    Step-by-step explanation:

    Point A is at -6 and point B is at 2.

    So, the distance between A and B = 2 - (-6) = 8

    point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4.

    Let the distance AC = x

    ∴ BC = 8 - x

    AC : CB = 3 : 4

    ∴[tex]\frac{AC}{CB} =\frac{3}{4} = \frac{x}{8-x}[/tex]

    Using cross multiplication

    3 (8-x) = 4x

    24 - 3x = 4x

    24 = 7x

    x = 24/7

    So, Point C = -6 + 24/7 = -18/7

    Point C at (-18/7)

  • The point C directed line segment from A to B is -18/7.

    Given that,

    A student wants to find point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4.

    Point A is at -6 and point B is at 2.

    We have to determine,

    The point C on the directed line segment from A to B.

    According to the question,

    Let, the distance AC be x,

    And BC = 8 - x

    The ratio of AC : BC = 3 : 4

    Therefore,

    [tex]\dfrac{AC}{BC} = \dfrac{3}{4} = \dfrac{x}{8-x}[/tex]

    Solving the equation by cross multiplication,

    [tex]3 (8-x) = 4x\\\\24 - 3x = 4x\\\\24 = 7x\\\\x = \dfrac{24}{7}[/tex]

    Then,

    Point C directed line segment from A to B is,

    [tex]= -6 + \dfrac{24}{7}\\\\= \dfrac{-42+24}{7}\\\\= \dfrac{-18}{7}[/tex]

    Hence, The point C directed line segment from A to B is -18/7.

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