How to compute distance of points to a line?

AI Thread Summary
The discussion revolves around calculating the distance from multiple points to a line defined by two coordinates. The user initially computed the line using the difference in coordinates and questioned whether they needed to derive the slope and intercept using the formula y=mx+b. After calculating the slope and intercept, the user sought assistance in determining the shortest distance from several x,y points to the line. Clarification was provided that the shortest distance is along a line perpendicular to the original line. The user confirmed that they intended to find the maximum distance from the points to the line. They referenced a formula from Wikipedia for calculating the distance from a point to a line and reported success in implementing it in Python, indicating that the problem was resolved.
msn009
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I have computed a line from point A to point B by just subtracting the coordinates as below:

line = np.array (x2-x1, y2-y1)

I am not sure if I need to form the formula for this line first by computing the slope and intercept but I continued my code as below, slope being m and b being the intercept from the formula y=mx+b

slope = (y2-y1)/(x2-x1)
b = (y2-y1) - (x2-x1)*slope

Now I am not sure how I can calculate the distance of several x,y points to this line.

can anyone help? thanks.
 
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Is this a homework problem?
 
no this is a self project
 
OK. When you say "the distance of several x,y points to this line" I assume you mean the standard "shortest distance", not just any old distance. If that's the case then it should be clear that the distance from any point to any line L is going to be on a line that is perpendicular to L, yes?
 
yes.. but just to be sure we are on the same page... say I have line L that I have computed as above. and I have x,y coordinates around this line or as you said that are perpendicular to this line and I now want to compute the distance of each x,y points to this line and take the point that has the maximum distance. I have attached the image for clarity. thanks
 

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i tried this formula and implemented it in python, and it seems to work so this problem is solved.
 

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