mail  mail@stemandmusic.in
    
call  +91-9818088802
Donate

Types of Lines in 2D

  1. A total of 8 Kinds of Lines can be laid out on a 2D Cartisean Plane which can be Classified into following 3 Types
    1. Lines that have Intercept on Only 1 of the Coordinate Axes
    2. Lines that have Non-Zero Intercepts on Both Coordinate Axes
    3. Lines that Pass through Origin and are Not Parallel or Perpendicular to Any Coordinate Axis.
  2. Based on their Cartesian Coordinate Equations, these 3 Types of Lines can be classified into following Subtypes. Please note that All Subtypes of a particular Line Type have Similar Kind of Cartesian Coordinate Equations.
    1. Lines that have Intercept on Only 1 of the Coordinate Axes. These are of following 2 Subtypes
      S.NoEquationSlopeInterceptsExplanation
      1. \( x=C \) Undefined x Intercept=C
      y Intercept=Undefined      		 These lines are perpendicular to X axis (and consequently parallel to Y axis). The line \(x=0\) is the Y axis.
      2. \( y=C \) 0 x Intercept=Undefined
      y Intercept=C      		 These lines are perpendicular to Y axis (and consequently parallel to X axis). The line \(y=0\) is the X axis.
    2. Lines that have Non-Zero Intercepts on Both Coordinate Axes. These are of following 4 Subtypes
      S.NoEquationSlopeInterceptsExplanation
      1. \(Ax+By-C=0\)
      OR
      \(-Ax-By+C=0\)       		\(\frac{-A}{B}\) x Intercept=\(\frac{C}{A}\)
      y Intercept=\(\frac{C}{B}\)      		 Both \(X\) and \(Y\) Intercepts are Positive. Slope is Negative. The Projection of the Origin on Line is in the 1st Quadrant.
      2. \(Ax-By+C=0\)
      OR
      \(-Ax+By-C=0\)       		\(\frac{A}{B}\) x Intercept=\(\frac{-C}{A}\)
      y Intercept=\(\frac{C}{B}\)      		 \(X\) Intercept is Negative. \(Y\) Intercept is Positive. Slope is Positive. The Projection of the Origin on Line is in the 2nd Quadrant.
      3. \(Ax+By+C=0\)
      OR
      \(-Ax-By-C=0\)       		\(\frac{-A}{B}\) x Intercept=\(\frac{-C}{A}\)
      y Intercept=\(\frac{-C}{B}\)      		 Both \(X\) and \(Y\) Intercepts are Negative. Slope is Negative. The Projection of the Origin on Line is in the 3rd Quadrant.
      4. \(-Ax+By+C=0\)
      OR
      \(Ax-By-C=0\)       		\(\frac{A}{B}\) x Intercept=\(\frac{C}{A}\)
      y Intercept=\(\frac{-C}{B}\)      		 \(X\) Intercept is Positive. \(Y\) Intercept is Negative. Slope is Positive. The Projection of the Origin on Line is in the 4th Quadrant.
    3. Lines that Pass through Origin and are Not Parallel or Perpendicular to Any Coordinate Axis. These are of following 2 Subtypes
      S.NoEquationSlopeInterceptsExplanation
      1. \( Ax-By=0 \)
      OR
      \( By=Ax \)       		\(\frac{A}{B}\) x Intercept=0
      y Intercept=0      		 These Lines are aligned in 1st and 3rd Quadrant. Slope is Positive
      2. \( Ax+By=0 \)
      OR
      \( By=-Ax \)       		\(\frac{-A}{B}\) x Intercept=0
      y Intercept=0      		 These Lines are aligned in 2nd and 4th Quadrant. Slope is Negative
Related Topics and Calculators
Types of Lines in 3D,    Types of Planes
  Home  |  TOC  |  Calculators
© Invincible IDeAS. All Rights Reserved