A Guide to Calculating the Distance from a Point to a Line | Formula and Steps

Distance from a point to a line

The distance from a point to a line is the shortest distance between the given point and the line

The distance from a point to a line is the shortest distance between the given point and the line. To find this distance, we can use the formula for distance between a point and a line.

Let’s say we have a point P with coordinates (x1, y1) and a line defined by an equation Ax + By + C = 0.

To find the distance, we can follow these steps:

1. Calculate the equation of the perpendicular line passing through point P. The equation of a line perpendicular to Ax + By + C = 0 is -Bx + Ay + D = 0, where D is a constant. We can substitute the coordinates of point P into this equation to find D.
-B(x1) + A(y1) + D = 0
D = B(x1) – A(y1)

2. Use the formula for distance between two parallel lines to find the distance between the line and the perpendicular line passing through point P. The formula is d = |C – D| / √(A^2 + B^2).

Distance = |C – (B(x1) – A(y1))| / √(A^2 + B^2)

So, the final formula to find the distance from a point to a line is:

Distance = |Ax1 + By1 + C| / √(A^2 + B^2)

This formula can be used for any point and line, as long as the equation of the line is given.

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