Table of Contents
How do you prove the distance from a point to a line?
Derivation of the Distance of a Point From a Line Consider a line L in XY−plane and K(x1 x 1 ,y1 y 1 ) is any point at a distance d from the line L. This line is represented by Ax + By + C = 0. The distance of a point from a line, ‘d’ is the length of the perpendicular drawn from K to L.
What is the shortest distance from a point to a straight line?
The shortest distance from a point to a line is always the path that’s perpendicular to the line, starting from the point.
How to find the shortest distance between two points on a plane?
So, y ′ = c 1 − c 2 = c o n s t a n t. The only curve which has a constant slope throughout is a straight line. Further, we can also integrate the above differential equation to yield the popular equation of straight line, i.e., y = m x + b. Hence, the shortest distance between two points on a 2D plane is indeed a straight line.
What is the shortest path between two points on a sphere?
A novel way to approach the problem is to use calculus of variations. The shortest path between two points (in a plane) is a straight line, the emphasis on the underlying geometry is important since the shortest path on a sphere is not a straight line but they are great circles, depicted here by green paths.
What does the shortest distance between two points is under construction mean?
“The shortest distance between two points is under construction.” Humans are always figuring out ways to expedite travel between two points. Prior to the advent of global travel, the shortest point was under construction – because transcontinental vehicles such as ships and planes, were not yet a reality.
What is the formula for the length of a curve?
Let us designate the length of the various curves y ( x) as s. Then, s can be given by s = ∫ A B ( d x) 2 + ( d y) 2 = ∫ a b 1 + ( d y / d x) 2 d x. Note that s is a function of y ( x). Recall that a function of function is referred as a functional.