# Distance of a Point from a Line

The distance of the point from the line is given by

Let be the inclination of the line as show in the given diagram, then its slope is given as

Squaring both sides of the above value of slope, we get

Draw a perpendicular from point to X-axis intersecting the line at point . Since the abscissa of is same as that of , so coordinates of point are , . In the triangle , and , so

Since the distance should be positive, so we must take the modulus of the right side of above equation, i.e.

Putting the value of from equation (i) in equation (ii), we get

Since the point lies on the line , so

Putting this value in equation (iii), we get

Example: Find the distance of the point from the line .

Since the given point is , so

Since the given line is , so

The required distance is