why do we need squaring and square root in the process of fnding the distance between two points.
4 Comments Already
January 16th, 2011 @7:06 pm
Simple answer is that we use triangle to find the distance between two points. We construct a right triangle and then use the pythagorean theorem
We can test why it can’t be with a simple problem.
(x1, y1) = (0, 0)
(x2, y2) = (3, 4)
your formula gives d = 7 when we know the answer must be 5 (those are the coordinates of a 3,4,5 triangle)
The distance you are calculating is the distance I would travel if I were to walk along the x axis and then the y axis or vice versa and not directly from point 1 to point 2.
January 16th, 2011 @7:13 pm
It can be. The formula you gave is also known as the one norm, taxicab norm and Manhattan norm. This is because the distance that this formula gives is similar to the distance it would take to go from one point to another in a car where all the streets are at right angles to each other.
The usual distance formula, on the other hand, gives the straight line distance between points.
January 16th, 2011 @7:27 pm
Distance formula is based upon theorem of Pythagoras (which has been running for a few years now)
d ² = (x2- x1) ² + (y2 – y1) ²
d = ? [ (x2 - x1) ² + (y2 - y1) ² ]
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Think of a right-angled triangle, with A being the right angle.
The distance from B to C is *not* AB + BC. It’s always much shorter to go in a straight line (the hypotenuse) than along one way, and up (or down) another.
By Pythagoras by know the actual distance BC is given by the formula
BC = sqrt (AB^2 + AC^2).
.