Sunday, May 4, 2008
A Geometry Tribute to Cinco de Mayo
Correction: Jonathan pointed out that I did not specify the order of the vertices. Thanks, Jonathan! Here is the revised version in which A and C are opposite vertices as are B and D:
Consider parallelogram ABCD, three of whose vertices are A(0,0), B(2,3) and D(3,2).
Find the coordinates of C and the area.
Of course, we expect our Geometry students to celebrate even more by generalizing:
Note: This has been revised for the reasons stated in the correction at the top.
Three of the vertices of a parallelogram ABCD are A(0,0), B(a,b) and D(b,a), where b>a>0.
(a) Show that vertex C has coordinates (b+a,b+a).
(b) Prove that this figure is actually a rhombus.
(c) Show that its area is b2 - a2. Can you find FIVE ways? (ok, that's a stretch but anything is possible on May 5th!).
Posted by Dave Marain at 8:20 AM 9 comments
Labels: area, geometry, investigations, parallelogram, rhombus