# 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 shown in the given diagram, and then its slope is given as

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

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

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

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

Since the point lies on the line , then

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