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