Hello friends.

There is a formula for area of a triangle in coordinate geometry which is as follows.

$\displaystyle \frac{1}{2}|x_1(y_2 - y_3)+x_2 (y_3 - y_1)+x_3 (y_1 - y_2)| $

I do not understand some aspects of this formula.

1. mod sign

2. I know the proof for all points lying in the first quadrant. Is there a proof that the area won't change for points lying in other quadrants? I could check for all the possible sets but that will take too long.

Are these two related?

Thanks.