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Math Help - Determine the equation of the median from vertex

  1. #1
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    Exclamation Determine the equation of the median from vertex

    ABC has the following co-ordinates: A(3,7)B(-1,-6) and C(-5,3). Determine the equation of the median from vertex C.

    This question is giving me a bit of trouble. If someone could please help me out i would greatly appreciate it.
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  2. #2
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    Quote Originally Posted by Scott9909
    ABC has the following co-ordinates: A(3,7)B(-1,-6) and C(-5,3). Determine the equation of the median from vertex C.

    This question is giving me a bit of trouble. If someone could please help me out i would greatly appreciate it.
    Part the First, find the coordinates of midpoint: By definition, the median from vertex C=(-5,3) is a line which joins the midpoint of side AB. But by the midpoint formula the midpoint of AB is (\frac{3-1}{2},\frac{7-6}{2})=(1,1/2). Thus, the median passes through points C=(-5,3) and (1,1/2).

    Part the Second, find the equation of median: Using the slope-point formula which states that the equation of a line passing through point (x_0,y_0) having slope m is y-y_0=m(x-x_0). Thus, the slope of (1,1/2),(-5,3) is m=-5/12. Thus, the equation of line is (use any point for (x_0,y_0))
    y+5=-5/12(x-3) Open and simplify,
    y=-\frac{5}{12}x-\frac{15}{4}
    Q.E.D.
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  3. #3
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    Im a bit confused on part 2.
    Do you have to find the slope of the line? Im not furmilur with the formula you put up. Ive been taught to do it Y=X2-X1/Y2-y1


    and i dont seem to be getting the same slope.
    Last edited by Scott9909; January 16th 2006 at 08:02 PM.
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  4. #4
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    That is exactly what I did (y_2-y_1)/(x_2-x_1). You mean the formula for the equation of the line?
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    Im not exactly sure. I really dont understand math that well.

    are you supposed to do y2-y/x2-x1 with your midpoint and C(-5,3)?

    And also if it is what is considered y2 and x2? C or the midpoint.

    Sorry if these questions are stupid.
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  6. #6
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    Quote Originally Posted by Scott9909
    Im not exactly sure. I really dont understand math that well.

    are you supposed to do y2-y/x2-x1 with your midpoint and C(-5,3)?

    And also if it is what is considered y2 and x2? C or the midpoint.
    Hello,

    you've got the answer to your problem already. I'll give you only a few additional informations:

    1. If you have 2 points P_1,\ P_2 with the coordinates P_1(x_1,\ y_1),\ P_2(x_2,\ y_2) then you'll get the midpoint M \left( \frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)

    2. A line through 2 points is described completely by the following equation:  \frac{y-y_1}{x-x_1} = \frac{y_2 - y_1}{x_2 - x_2}

    Solve this equation for y and you'll get:  y = \frac{y_2 - y_1}{x_2 - x_2}\cdot (x-x_1) + y_1 where   \frac{y_2 - y_1}{x_2 - x_2} is the slope of the line.

    I hope that these additional remarks helped a little bit.

    Greetings

    EB
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