(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>

Are these questions expected to be solved

solely via a calculator? Are these supposed to be approached via programming? Is some pencil to paper math allowed to simplify this? I worked an answer (A = 285 19/25 ?) by first rotating x+y=15 to y=15 then rotating the other lines slopes CCW by the same amount. Finding the intersection of these transformed lines yield the base, height of the triangle.