Point of intersection of two lines
The coordinates of the point of intersection of the two intersecting lines a1x + b1y + c1= 0 and a2x + b2y + c2 = 0 are
However, to obtain the point of intersection, we are required to just solve the equations of the straight lines given as we do in the case of simultaneous equations.
Condition of concurrency of three linesThree lines are said to be concurrent, if they pass through a common point, i.e., if they meet at a point. The condition for three lines a1x + b1y + c1 = 0, a2x + b2y + c2 = 0 and a3x + b3y + c3 = 0 is
a1(b2c3 - b3c2) + b1(c2a3 - c3a2) + c1(a2b3 - a3b2) = 0
Length of perpendicularThe length of perpendicular (p) from (X1, Y1) on the line AX + BY + C = 0 is:
Distance between two parallel lines
The distance between two parallel lines AX + BY + C1 = 0 and AX + BY + C2 = 0 is given by
Conditions for points to be collinear
If three points A, B, C are co-linear, then any one of the following conditions should be true:
- Area of triangle ABC = 0
- Slope of AB = slope of BC = slope of AC
- AB + BC = AC
Depending upon the points given, we can use any one of three to check if the points are collinear. It should also be mentioned that if one of these conditions is true, then other two will definitely be true.