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Math Help - Function and Geometry [Eleventh Grade]

  1. #1
    bekridu19
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    Function and Geometry [Eleventh Grade]

    The function defined on R by f(x)= (2/3)x+2

    And cf his graphic representation in an orthonormal mark (o; i; j)

    On the X axis, we consider points A, B and H of respective abscissas 3, -3 and x (x belongs R)

    Or C the point of Cf of the same abscissa as A and M the point of Cf of abscissa x


    1) Make the complete figure ?

    2) Calculate the distances AH and MH according to x and by means of the absolute values ?

    3) To determine for which value (s) of x the areas of triangles CHA and MOB is equal ?


    Please Anyone for help me, Can you draw this graphic please please and represents all points A B H M and C
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by bekridu19 View Post
    The function defined on R by f(x)= (2/3)x+2

    And cf his graphic representation in an orthonormal mark (o; i; j)
    On the X axis, we consider points A, B and H of respective abscissas 3, -3 and x (x belongs R)
    Or C the point of Cf of the same abscissa as A and M the point of Cf of abscissa x

    1) Make the complete figure ?
    2) Calculate the distances AH and MH according to x and by means of the absolute values ?
    3) To determine for which value (s) of x the areas of triangles CHA and MOB is equal ?


    ...
    to #1: see attachment

    to #2:

    |\overline{AH}| = |x-(-3)| = |x+3|

    |\overline{HM}| = \left|\frac23 x +2\right|

    to #3:

    area_{AHM} = \frac12 \cdot (x+3) \cdot \left(\frac23 x +2 \right) . Right triangle, painted red.

    area_{ABM} = \frac12 \cdot 6 \cdot \left(\frac23 x +2 \right) Triangle painted blue.

    The areas of both triangles are equal if:

    x+3 = 6~\vee~ \frac23 x +2 =0~\implies~\underbrace{x = 3}_{\text{maximum}} ~\vee~ \underbrace{x=-3}_{\text{minimum}}
    Attached Thumbnails Attached Thumbnails Function and Geometry [Eleventh Grade]-fl_zweidreiecke.gif  
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