Multiplying points in the plane

It is easy to add points in the plane “coordinatewise”, that is, by writing (x,y)+(z,w)=(x+z,y+w). This even has a very nice geometric interpretation: completing the parallelogram with first three corners (0,0), (x,y), and (z,w). But it isn’t easy to multiply points because the simple rule (x,y)*(z,w)=(xz,yw) doesn’t allow division. In this activity we looked for something better.

Check out our handout!