CBSE Class 11 Maths Notes Chapter 10 Straight Lines

A straight line is a fundamental geometric concept defined as a path traced by points moving in a constant direction with zero curvature. In simpler terms, it's the shortest distance between two points. This concept is crucial in various fields, from mathematics and physics to engineering and architecture. Understanding straight lines allows us to analyze and describe the relationships between points in space efficiently. Whether it's plotting coordinates on a graph or determining the trajectory of an object, the notion of a straight line serves as a fundamental building block for many mathematical and scientific applications.

General Form of a Line

The relation between variables such as x and y agrees with all points on the curve. The general form of the equation of a straight line is given as: Ax + By + C = 0 Where, A, B, and C are constants and x, y are variables.

Slope of a Line

In geometry, the slope or gradient of a line, denoted by 'm', is a measure of its inclination or steepness. When represented by the angle θ, the tangent of θ, denoted as 'tan θ', represents the slope of the line. However, it's important to note that the slope is undefined when the line is vertical, as the tangent of 90 degrees is undefined. Conversely, a horizontal line has a slope of 0, as the tangent of 0 degrees is 0. Therefore, for any line other than vertical, its slope 'm' can be expressed as 'tan θ', where θ is the angle of inclination, and θ is not equal to 90 degrees. Understanding slope is crucial in various mathematical and scientific contexts, such as calculating rates of change, analyzing gradients in terrain, and determining the direction of vectors in physics.

Slope Intercept Form

The straight - line equation  in slope-intercept form is given as:

Y = mx + C

Where m represents the slope of the line and C is the y-intercept.

Shortest Straight Line Distance

The shortest straight line distance between two points say P and Q having coordinates (P₁, Q₁) and (P₂, Q₂) is expressed as:

Equation of Line – Different Forms