## Straight Lines

# Distance of a Point From a Line

- The perpendicular distance from a point (x
_{1}y_{1}) 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 (x
_{1}y_{1}) and origin lies on the same or opposite side of a line L = ax + by + c = 0 according as c. L_{11}> 0 or c. L_{11}< 0 - The point A (x
_{1}y_{1}) 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 (x
_{1}y_{1}) 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 (x_{1} , y_{1}) 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 + C_{1} = 0 and Ax + By + C_{2} = 0 is given by d = \tt \frac{\mid C_{1}-C_{2}\mid}{\sqrt{A^{2}+B^{2}}}.