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Shows how to find the perpendicular distance from a point to a line, and a proof of the formula.
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.
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.
The perpendicular distance, 𝐷, between a point 𝑃 (𝑥, 𝑦, 𝑧) and a line with direction vector ⃑ 𝑑 can be found by using the formula 𝐷 = ‖ ‖ 𝐴 𝑃 × ⃑ 𝑑 ‖ ‖ ‖ ‖ ⃑ 𝑑 ‖ ‖, where 𝐴 is any point on the line.
find the possible equations for a line at a specified perpendicular distance from a point, find the area of a given polygon on the coordinate plane using the concept of the distance between a point and a line.
For example, Find the distance between the point (2,6) and the line y=−2x. This tells me that the slope of the perpendicular line is 1/2. The equation for my second line would then be, (6) = 1/2*(2) + b.
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.
