posted by Jane .
The vertices of quadrilateral ABCD are (A(1,1), B(1,5), C(5,5) and D(7,1). You want to transform ABCD into a parallelogram by only moving point B. A parallelogram is a four-sided figure with both pairs of opposite sides parallel. What should be the new x-coordinate of point B?
As it stands now, A and D are on the same horizontal line, and B and C are on the same horizontal line.
However, we want to move only point B. So, if we keep BC parallel to AD, then we want to have BC the same length as AD, which is 6.
Right now, the length of BC is 5-1 = 4. So, to increase the length to 6, staying on the line y=5, we move B to (-1,5).
Now we have two parallel sides, AD and BC of length 6. Note also that now AB and CD are parallel and the same length, so we have a parallelogram.