Parallelograms in the coordinate plane


Construct a figure like this one with Sketchpad using the following steps.



In the graph menu,



Then, letting A be the origin, draw segments AB and AC.  Construct a parallelogram ABDC.





Now let E be the intersection of the y-axis and the line CD (i.e., the y-intercept).  Construct point F so that ABFE is a parallelogram.




Getting a Formula

Now follow this same construction process but this time instead of numbers, use letters for the coordinates.  Let B = (a,b) and C = (c, d).



You should have a formula for the area of the parallelogram ABDC without doing a gruesome calculation involving the height of ABDC because you found the area of a simpler parallelogram with the same area.  You may find the expression in the formula looks familiar from another course.