Problem

(Geometry: intersecting point) Two points on line 1 are given as (x1, y1) and (x2, y2) and...

(Geometry: intersecting point) Two points on line 1 are given as (x1, y1) and (x2, y2) and on line 2 as (x3, y3) and (x4, y4), as shown in Figure 3.8a–b. The intersecting point of the two lines can be found by solving the following linear equation:

(y1 - y2)x - (x1 - x2)y = (y1 - y2)x1 - (x1 - x2)y1

(y3 - y4)x - (x3 - x4)y = (y3 - y4)x3 - (x3 - x4)y3

This linear equation can be solved using Cramer’s rule (see Programming Exercise). If the equation has no solutions, the two lines are parallel (Figure 1).

Write a program that prompts the user to enter four points and displays the intersecting point. Here are sample runs:

FIGURE 1 Two lines intersect in (a and b) and two lines are parallel in (c).