Enter the coordinates of the point (x1,y1) and the a,b, and c values of the line equation (ax+by+c=0) into the Point to Line Distance Calculator. The calculator will evaluate and display the Point to Line Distance. 

Point to Line Distance Formula

The following formula is used to calculate the Point to Line Distance. 

PLD = |a*x1+b*y1+c| / sqrt ( a^2 + b^2)
  • Where PLD is the Point to Line Distance
  • x1,y1 is the coordinates of the point (x1,y1) 
  • a,b,c are the a,b, and c values of the line equation (ax+by+c=0) 

How to Calculate Point to Line Distance?

The following example problems outline how to calculate Point to Line Distance.

Example Problem #1:

  1. First, determine the coordinates of the point (x1,y1).
    • The coordinates of the point (x1,y1) is given as: 10,3.
  2. Next, determine the a,b, and c values of the line equation (ax+by+c=0).
    • The a,b, and c values of the line equation (ax+by+c=0) is provided as: 5,6,12.
  3. Finally, calculate the Point to Line Distance using the equation above: 

PLD = |a*x1+b*y1+c| / sqrt ( a^2 + b^2)

The values given above are inserted into the equation below and the solution is calculated:

PLD = |5*10+6*3+12| / sqrt ( 5^2 + 6^2) = 10.243


Example Problem #2: 

For this problem, the variables needed are provided below:

coordinates of the point (x1,y1) = 10,12

a,b, and c values of the line equation (ax+by+c=0) = 5,9,.5

This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer. 

PLD = |a*x1+b*y1+c| / sqrt ( a^2 + b^2) = ?