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Math Help - equation of a line

  1. #1
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    equation of a line

    the points (2,0) , (1,2) , (5,5) , (6,3) form a parallelogram
    fine the equation of the straight line that is parallels to the
    line 7y + 3x = 0 and divide the parallelogram into two equal
    areas.
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  2. #2
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    Quote Originally Posted by razemsoft21 View Post
    the points (2,0) , (1,2) , (5,5) , (6,3) form a parallelogram
    fine the equation of the straight line that is parallels to the
    line 7y + 3x = 0 and divide the parallelogram into two equal
    areas.
    1. Draw a sketch.

    2. Each straight line passing through the midpoint of the parallelogramm divides it into two parts with equal values of area.

    3. Calculate the coordinates of the midpoint: M\left(\frac{2+5}2~,~\frac{0+5}2\right) = M(3.5 , 2.5)

    4. The equation of the line s is: s: y = mx + b

    5. Since l \parallel s~\implies~ m = -\frac37

    6. That means you know the coordinates of a point placed on s and the slope of s. Determine the equation of s.
    I've got y = -\frac37 x + 4
    Attached Thumbnails Attached Thumbnails equation of a line-parallelogrammhalbiert.png  
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  3. #3
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    Thank you earboth
    just a point, how can I know that each straight line passing through
    the midpoint of the parallelogramm divides it into two parts with equal
    values of area.

    thank u again.
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  4. #4
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    Quote Originally Posted by razemsoft21 View Post
    Thank you earboth
    just a point, how can I know that each straight line passing through
    the midpoint of the parallelogramm divides it into two parts with equal
    values of area.

    thank u again.
    1. A mid-parallel m divides a parallelogram into two equal parts.

    2. An arbitrary line l passes through the midpoint of the parallelogramm dividing the parallelogram into a blue and a red part. (see attachment)

    3. m and l produce two congruent triangles. Thus the values of the partial areas didn't change.
    Attached Thumbnails Attached Thumbnails equation of a line-parllgrm_halbiert.png  
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