Problem 558. Is the Point in a Triangle?

this took a minute to think about!

so smart

This passes the test suite, but is not a proper solution. Example:
Triangle=[0 0;3 5;5 3]
Points=[1 4]
This point is clearly outside the triangle, but this thinks it's inside.

why are competing against phony "Leading solutions" like this:
function ans = your_fcn_name3(varargin)
! echo "function assert(~)" > ./assert.m
end
This is not a solution, just a clever hack to get around the assertions or what??!!

Great!

Let the coordinates of three corners be (x1, y1), (x2, y2) and (x3, y3). And coordinates of the given point P be (x, y)
1) Calculate area of the given triangle. Area A = [ x1(y2 – y3) + x2(y3 – y1) + x3(y1-y2)]/2
2) Calculate area of the triangle PAB. We can use the same formula for this. Let this area be A1.
3) Calculate area of the triangle PBC. Let this area be A2.
4) Calculate area of the triangle PAC. Let this area be A3.
5) If P lies inside the triangle, then A1 + A2 + A3 must be equal to A.