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26 November, 07:49

A rhombus is on a coordinate plane and has one of its sides modeled by the equation 3y - 4x = 35. determine which of the following equations could model the opposite side of the rhombus. Select all that apply.

A. y = 4/3 x + 16/3

B. y - 3 = 3/4 (x - 8)

C. 8x - 6y = 38

D. 9y = 12x - 27/14

E. 2x + y = - 5

F. 4x - 3y = 12

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Answers (1)
  1. 26 November, 08:01
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    A. y = 4/3 x + 16/3.

    C. 8x - 6y = 38

    D. 9y = 12x - 27/4

    F. 4x - 3y = 12.

    Step-by-step explanation:

    A rhombus has parallel opposite sides so the lines will have the same slope as:

    3y - 4x = 35

    We convert to slope - intercept form:

    3y = 4x + 35

    y = 4/3 x + 35/3

    - so the slope of this line is 4/3.

    Now the opposite side will also have a slope of 4/3 but a different y-intercept.

    So A. y = 4/3 x + 16/3 is one of the required equations.

    8x - 6y = 38

    6y = 8x - 38

    y = 4/3 x - 38/6. (C)

    - The same slope, so this could also be one of the required equations.

    9y = 12x - 27/4

    y = 4/3 x - 27/36 (D)

    - so this could also be one of the required equations.

    4x - 3y = 12

    3y = 4x - 12

    y = 4/3 x - 4.

    This is one also (F).

    B and E have slopes of 3/4 and - 2 so could not be models for the opposite side.
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