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The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line.
Shows how to find the perpendicular distance from a point to a line, and a proof of the formula.
Learn how to find the perpendicular distance of a point from a line easily with a formula. For the formula to work, the line must be written in the general form.
What is the distance between point \(P\) and line \(L\) in the diagram? The length of each line segment connecting the point and the line differs, but by definition the distance between point and line is the length of the line segment that is perpendicular to \(L\).
The distance between a point and a line, is defined as the shortest distance between a fixed point and any point on the line. It is the length of the line segment that is perpendicular to the line and passes through the point.
In this explainer, we will learn how to find the perpendicular distance between a point and a straight line or between two parallel lines on the coordinate plane using the formula. By using the Pythagorean theorem, we can find a formula for the distance between any two points in the plane.
Perpendicular Distance from Point to Line. The shortest distance between point and line is calculated by finding the length of the perpendicular drawn from the point to the line. Consider the line l: $Ax + By + C = 0$ and point $P(x₁, y₁)$. Note that PQ is the perpendicular from point P to line l. Let l$(PQ) = d$.
