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: $\displaystyle M\left(\frac{2+5}2~,~\frac{0+5}2\right) = M(3.5 , 2.5)$
4. The equation of the line s is: s: y = mx + b
5. Since $\displaystyle l \parallel s~\implies~ m = -\frac37$
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 $\displaystyle y = -\frac37 x + 4$
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.