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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.
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.
Shows how to find the perpendicular distance from a point to a line, and a proof of the formula.
The equation of a plane perpendicular to the line is $$x+y+z=a.$$ If this plane passes through $(2,2,1)$ then $a=5$. So the plane $x+y+z=5$ intersects the line when $$3t+6=5$$ so $t=-\frac{1}{3}$ and now you just need the distance between $S$ and $(\frac{5}{3},\frac{5}{3}, \frac{5}{3})$.
The distance between a point \(P\) and a line \(L\) is the shortest distance between \(P\) and \(L\); it is the minimum length required to move from point \( P \) to a point on \( L \). In fact, this path of minimum length can be shown to be a line segment perpendicular to \( L \).
distance from a point to a line. 點到直線距離. Theorem 25.1 {P = P(x0, y0) L = L(x, y) = Ax + By + C = 0, A2 + B2 ≠ 0 ⇓ d(P, L) = |Ax0 + By0 + C| √A2 + B2. https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line. https://highscope.ch.ntu.edu.tw/wordpress/?p=47407.
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.
