Posted by Jane on Friday, December 30, 2011 at 3:49pm.
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 foursided figure with both pairs of opposite sides parallel. What should be the new xcoordinate of point B?

math  Steve, Friday, December 30, 2011 at 4:31pm
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 51 = 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.