Straight Lines

Straight Lines is a fundamental and an important topic under Co-ordinate Geometry.

Several methods have been developed by mathematicians to uniquely locate the position of the points in space. The easiest and most widely used one is the Cartesian coordinate system, which is based on mutually perpendicular axes. In this chapter you will learn about this system: locating the points in this system and finding equations of line passing through these points.

If we say a line passes through two given points, we are imposing two conditions on this line. The conditions can be imposed in several other manners also e.g. we may say that a line passes through one point and is perpendicular to another line. These two conditions are sufficient to uniquely known our line. In this chapter you will also learn various manners of imposing conditions and finding the equation of line under those conditions.

Having known the line uniquely in space we shall try to a lots timings with it e.g. divide it in a given ratio, find distances of other points or lines from it, find the angles, which this line make with some straight line.

“Straight Lines” is one of the easiest and important chapters of Co-ordinate Geometry in the Mathematics syllabus of IIT JEE, AIEEE and other engineering examinations. These laws are not new to any aspirant as he is using the principles even in day to day life.

The chapter is important not only because it fetches 2-3 questions in most of the engineering examination but also because it is prerequisite to the other chapters of Co-ordinate Geometry.

Topics Covered: 

• Representation of Points in Plane
• Distance between two Points
• Centroid Incentre and Circum Centre
• Area of Triangle
• Standard Equations of Straight Line
• Different Forms of Line
• Examples based on Straight Line
• Angle between two Straight Lines
• Equation of Locus
• Examples on Angle between two Straight Lines
• Length of Perpendicular from Point on Line
• Distance between two Parallel Lines
• Examples on Distance between two Parallel Lines
• Family of Lines
• Concurrency of Straight Lines
• Position of two Points with Respect to a given Line
• Angle Bisectors
• Pair of Straight Lines
• Angle between Pair of Lines
• Combined Equations of Angle Bisectors of Lines
• Joint Equation of Pair of Lines