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) = ?