The slope of AB is =3/4 The slope of CD is 12/a Determine the value of a if AB丄CD?

7 Answers

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  • 2 months ago

    AB_|_CD=>(3/4)(12/a)=-1=>9/a=-1=>a=-9.

  • alex
    Lv 7
    2 months ago

    Rule

    If (the slope of AB)*(the slope of CD)=-1

    then

    AB丄CD

  • Philip
    Lv 6
    2 months ago

    Suppose slope of AB = m. Then slope of CD which is perpendicular to AB is -(1/m), m =/= 0.

    Here m = (3/4) so slope of CD = -(4/3) = 12/a. Then a = -(3/4)12 = -9.

  • Anonymous
    2 months ago

    When solving questions as such, always keep in mind these two rules:

    1) Parallel lines have the same slope.

    2) Perpendicular lines have opposite reciprocals slopes:

        m_1 x m_2 = -1

    In this questions the lines are perpendicular so the second rule will be used:

    AB丄CD

    3/4 x 12/a = -1

    dived 3/4 on both sides

    12/a = -4/3

    criss cross multiplication

    -4a = 36

    divide -4 on both sides

    a = -9

    Your answer is -9.

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  • sepia
    Lv 7
    2 months ago

     If two lines are perpendicular, the product of their gradients is -1.  

     i.e. (3/4) x (12/a) = -1

    Hence, 9/a = -1 

    So, a = -9

  • ?
    Lv 7
    2 months ago

    Since AB ⊥ CD, the slope of CD must equal the negative reciprocal of the slope of AB.Since the slope of AB = 3/4, the slope of CD must equal

    .....12......-4

    .....---- = -----

    ......a........3

    Therefore,

    .....a = (12•3)/(-4)

    .....a = -9..................ANS

  • 2 months ago

    Two lines are perpendicular if their slopes are negative reciprocals.

    Therefore, the slope of CD is -4/3.

    12/a = -4/3.

    Cross-multiplying gives: -4a = 36.

    a = -9

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