21625_IntersectingLines

We all know that a pair of distinct points on a plane defines a line and that a pair of lines on a plane will intersect in one of three ways:

1) no intersection because they are parallel,

2) intersect in a line because they are on top of one another (i.e. they are the same line),

3) intersect in a point.

In this problem you will use your algebraic knowledge to create a program that determines how and where two lines intersect.

Your program will repeatedly read in four points that define two lines in the x-y plane and determine how and where the lines intersect. All numbers required by this problem will be reasonable, say between -1000 and 1000.

The first line contains an integer N between 1 and 10 describing how many pairs of lines are represented. The next N lines will each contain eight integers. These integers represent the coordinates of four points on the plane in the order x₁  y₁  x₂  y₂  x₃  y₃  x₄  y₄. Thus each of these input lines represents two lines on the plane: the line through (x₁, y₁) and (x₂, y₂) and the line through (x₃, y₃) and (x₄, y₄). The point (x₁, y₁) is always distinct from (x₂, y₂). Likewise with (x₃, y₃) and (x₄, y₄).

There should be N+2 lines of output. The first line of output should read INTERSECTING LINES OUTPUT. There will then be one line of output for each pair of planar lines represented by a line of input, describing how the lines intersect: none, line, or point. If the intersection is a point then your program should output the x and y coordinates of the point, correct to two decimal places. The final line of output should read "END OF OUTPUT".

5
0 0 4 4 0 4 4 0
5 0 7 6 1 0 2 3
5 0 7 6 3 -6 4 -3
2 0 2 27 1 5 18 5
0 3 4 0 1 2 2 5

INTERSECTING LINES OUTPUT
POINT 2.00 2.00
NONE
LINE
POINT 2.00 5.00
POINT 1.07 2.20
END OF OUTPUT