407226: GYM102697 197 Three Lines

You're given three lines on the coordinate plane. No pairs of the lines are parallel.

Figure out the area of the triangle formed by the intersection points of the three lines. In other words, label the points of interesection of lines 1 and 2, lines 1 and 3, and lines 2 and 3, $$$A$$$, $$$B$$$, and $$$C$$$, respectively. Then, your task is to find the area of triangle $$$ABC$$$.

The input consists of three lines, each containing the equation for one of the lines, in $$$y = mx + b$$$ form, where $$$m$$$ represents the slope of the line, and $$$b$$$ represents the y-intercept of the line.

Output a single decimal number representing the area of the triangle formed by the intersection points of the three lines. Do not round your answer. Your answer doesn't have to be exactly equal to ours; as long as it's within a few decimal places it will be judged as correct.

y = 2x + 3
y = -2x + 9
y = x - 2

28.166666666666664

y = 2x + 3
y = -2x + 9
y = -x - 27

793.5000000000001

y = 2x + 3
y = -2x + 90
y = 7x - 2

478.4027777777778

Here is the graph of the first example case: