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Math Help - Geometry Properties of a Triangle Help

  1. #1
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    Post Properties of a Triangle

    I need help on using midpoints to draw a triangle... here's the question

    "the midpoints of the sides of a triangle are L(4,2), M(2,3), AND N(5,4). What are the coordinates of the vertices of the triangle?"

    I understand that you find the slope of each side, but what do you do after that? Please help and thanx
    Last edited by I'm_Schuyler; December 3rd 2008 at 08:19 PM.
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  2. #2
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    Quote Originally Posted by I'm_Schuyler View Post
    I need help on using midpoints to draw a triangle... here's the question

    "the midpoints of the sides of a triangle are L(4,2), M(2,3), AND N(5,4). What are the coordinates of the vertices of the triangle?"

    I understand that you find the slope of each side, but what do you do after that? Please help and thanx
    1. Let A, B and C denote the vertices of the triangle you are looking for.

    2. Draw the triangle LMN.

    3. The side of triangle ABC which passes through L must be parallel to MN:

    Calculating the slope MN: m_{MN}=\dfrac{3-4}{2-5}=\dfrac13
    Calculating the equation of the line through L:
    y-2=\frac13 (x-4)~\implies~\boxed{y = \frac13x + \frac23}

    4. Do just the same with the points M and N. You then have 3 equations of three lines.

    5. Calculate the coordinates of the intersection points of these three lines.
    Attached Thumbnails Attached Thumbnails Geometry Properties of a Triangle Help-dreieck_asmitten3eck.png  
    Last edited by earboth; December 3rd 2008 at 11:05 PM. Reason: added a sketch
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  3. #3
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    3. The side of triangle ABC which passes through L must be parallel to MN:

    I dont get how the line passing through L is parallel to MN.
    Any explanation?
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  4. #4
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    Quote Originally Posted by syathish View Post
    3. The side of triangle ABC which passes through L must be parallel to MN:

    I dont get how the line passing through L is parallel to MN.
    Any explanation?
    There is a theorem whos name is (literally translated) "mid parallel in triangles theorem ":

    "The connection between 2 midpoints of 2 sides in a triangle is parallel to the third side and has half the length of the third side."

    I've used this theorem.
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  5. #5
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    Quote Originally Posted by earboth View Post
    There is a theorem whos name is (literally translated) "mid parallel in triangles theorem ":

    "The connection between 2 midpoints of 2 sides in a triangle is parallel to the third side and has half the length of the third side."

    I've used this theorem.
    Thnx fo reminding me m8
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