 # 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

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

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}}}.