How to compute distance of points to a line?

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SUMMARY

The discussion focuses on calculating the distance from multiple points to a line defined by two points, A and B, using Python's NumPy library. The user computes the line vector and the slope-intercept form of the line but seeks clarification on determining the shortest distance from various (x, y) coordinates to this line. The solution involves using the formula for the distance from a point to a line, which is confirmed to work effectively in Python. The user successfully implements this formula and resolves their query.

PREREQUISITES
  • Understanding of vector mathematics and line equations
  • Familiarity with Python programming and NumPy library
  • Knowledge of slope-intercept form of a line (y = mx + b)
  • Basic concepts of distance measurement in geometry
NEXT STEPS
  • Implement the distance formula from a point to a line in Python
  • Explore the use of NumPy for vectorized operations in distance calculations
  • Study the geometric interpretation of distances in 2D space
  • Learn about optimization techniques for handling large datasets of points
USEFUL FOR

Data scientists, Python developers, and anyone interested in computational geometry or spatial analysis will benefit from this discussion.

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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