Intersecting Lines |

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 . Thus each of these input lines represents two lines on
the plane: the line through and and the line through
and . The point is always distinct from
. Likewise with and .

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