(08-12-2015 04:22 PM)Peter Murphy Wrote: The following problem, from the 2013 Houston calculator exam, seems conceptually simple to solve, but the manipulations necessary to solve it from start to finish on the 50g are not so obvious:

14. There are 3 points of intersection of pairs of the lines 2x+3y=4, 7x-2y=3 and

x+y=15. Give the area of the triangle determined by these three points.

It seems clear that the "shoelace formula" of Meister and Gauss* is needed, and a little program to apply that would be nice.

Peter

* <https://en.wikipedia.org/wiki/Shoelace_formula>

We could also seek the points {A, B, C} of the intersections of d1 and d2, d2 and d3, d1 and d3 (with solve for example) and then S=1/2.||AB /\ AC ||