Straight Lines

Distance of a Point From a Line

  • The perpendicular distance from a point (x1 y1) to the line ax + by + c = 0 is \tt \begin{vmatrix}\frac{ax_{1}+by_{1}+c}{\sqrt{a^{2}+b^{2}}} \end{vmatrix}
  • A point A (x1 y1) and origin lies on the same or opposite side of a line L = ax + by + c = 0 according as c. L11 > 0 or c. L11 < 0
  • The point A (x1 y1) lies above or below the line L = ax + by + c = 0 according as \tt \frac{L_{11}}{b}>0 \ or \ \frac{L_{11}}{b}< 0
  • The distance of a point (x1 y1) from the line L = ax + by + c = 0 measured along a line making an angle ‘∝’ with x – axis is \tt \begin{vmatrix} \frac{ax_{1}+by_{1}+c}{a\cdot cos \propto + b \sin \propto } \end{vmatrix}

View the Topic in this video From 00:40 To 55:58

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1. The perpendicular distance (d) of a line Ax + By + C = 0 from a point (x1 , y1) is given by d = \tt \frac{\mid Ax_{1}+By_{1}+C\mid}{\sqrt{A^{2}+B^{2}}}.
2. Distance between the parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by d = \tt \frac{\mid C_{1}-C_{2}\mid}{\sqrt{A^{2}+B^{2}}}.