CareerCup

Compare slope. If it's the same they are parallel.

Here is the solution to find lines are parallel, perpendicular or Intersecting lines

Example 1:
line1: points (–1, –2) and (1, 2)
line2: points (–2, 0) and (0, 4)
Answer => "Lines are Parallel!!"

Example 2:
line1: points (0, –4) and (–1, –7)
line2: points (3, 0) and (–3, 2)
Answer => "Lines are Perpendicular!!"

Example 3:
line1: points (–4, 2) and (0, 3)
line2: points (–3, –2) and (3, 2)
Answer => "Lines Intersects!!"

static void Main( string[] args)
        {
            decimal m1 = FindSlope(0, -4, -1, -7);
            decimal m2 = FindSlope(3, 0, -3, 2);

            if (m1 == m2)
                Console.WriteLine( "Lines are Parallel!!" );
            else if ((1 / m1) == (-m2))
                Console.WriteLine( "Lines are Perpendicular!!" );
            else
                Console.WriteLine( "Lines Intersects!!" );

            Console.ReadKey();
        }

        static decimal FindSlope( decimal x1, decimal y1, decimal x2, decimal y2)
        {
            return ((y2 - y1) / (x2 - x1));
        }

My answer suggestion :

Equations of two lines:
A1x + B1y = C1
A2x + B2y = C2
To find the point at which the two lines intersect, we simply need to solve the two equations for the two unknowns, x and y.

    double det = A1*B2 - A2*B1
    if(det == 0){
        //Lines are parallel
    }else{
        double x = (B2*C1 - B1*C2)/det
        double y = (A1*C2 - A2*C1)/det
    }

considering lines, not line segment we can have 3 cases for a given pair of lines
y=m1*x+c1
y=m2*x+c2
case1) lines do not intersect if both the lines are parallel to each other that is
m1=m2 and c1 != c2
case2)lines are collinear when m1=m2 and c1= c2 in this case there will be more than one point where line intersects(all the points on the line infinite)
case3) for all other case there will be exact one intersection point
xs=(c1-c2)/(m2-m1) and ys=m1*xs+c1 where (xs,ys) is intersection point..

Let say y=a+bx is the equation of a line. This line intersects with x=0 at (0,a) and with x=1 at (1,a+b). Now for two lines y1=a1+b1x1 and y2=a2+b2x2 to intersect one the following two conditions should satisfy:
1. either a1>a2 and a1+b1<a2+b2 OR
2.a1<a2 and a1+b1>a2+b2

Equations of two lines:
a1X + b1Y = c1
a2X + b2Y = c2

def areParallel(a1,b1, a2,b2):
	if (a1==0 and a2==0) or (b1==0 and b2==0):
		return True
	
	if (a1*b2 == a2*b1):
		return True

	return False