# Point of intersection of two lines

The coordinates of the point of intersection of the two intersecting lines

*a*_{1}*x*+*b*_{1}*y*+*c*= 0 and_{1}*a*_{2}*x*+*b*_{2}*y*+*c*= 0 are_{2}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 lines

Three 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*a*

_{1}*x*+

*b*

_{1}*y*+

*c*= 0,

_{1}*a*

_{2}*x*+

*b*

_{2}*y*+

*c*

_{2}_{ }= 0 and

*a*

_{3}*x*+

*b*

_{3}*y*+

*c*= 0 is

_{3}*a*(

_{1}*b*

_{2}*c*-

_{3}*b*

_{3}*c*) +

_{2}*b*(

_{1}*c*

_{2}*a*-

_{3}*c*

_{3}*a*) +

_{2}*c*(

_{1}*a*

_{2}*b*-

_{3}*a*

_{3}*b*) = 0

_{2}# Length of perpendicular

The length of perpendicular (*p*) from (

*X*

_{1},

*Y*) on the line

_{1}*AX*+

*BY*+

*C*= 0 is:

# Distance between two parallel lines

The distance between two parallel lines

*AX*+*BY*+*C*= 0 and_{1}*AX*+*BY*+*C*= 0 is given by_{2}# 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.