perpendicular distance calculator - step by step calculation, formula & solved example to calculate the distance from a point or coordinates (x_{1}, y_{1}) to line Ax + By + C = 0 in a two dimensional space or XY plane. x_{1}, y_{1} is the point and the Ax + By + C = 0 is the line in the two dimensional space or XY plane.
Formula
The below formula is used to find the perpendicular length from a point to a line.
Solved Example
This below solved example let users to understand how the example values are being used in this calculation to determine perpendicular length from a point to line.
Problem:
Find the perpendicular distance from the point (5, 6) to a line 7x + 9y + 12 = 0.
Solution:
Let's consider x_{1} = 5 & y_{1} = 6
Apply the values in the formula
= ((7 x 5) + (9 x 6) + 12) / √(7^{2} + 9^{2})
= 101/√(130)
Perpendicular Length = 8.8583
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