1. 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.

2. Originally Posted by razemsoft21
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 $y = -\frac37 x + 4$

3. 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.

4. Originally Posted by razemsoft21
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.