# Answer to a question no one asked

Dar Scott dsc at swcp.com
Tue Jan 25 13:59:10 EST 2005

```On Jan 6, 2005, at 8:40 AM, James Hurley wrote:

> What is the perpendicular distance between a point and a line?

I was grading my daughter's math papers and thought of a couple things
related to this.

1.  It is possible to create the general line parameters A, B and C of
Ax + By + C =0 without any division, so no 'if' is needed.  This can be
normalized by dividing by sqrt( A^2 + B^2 ), and since both A and B
can't be 0 (assuming the two points defining the line are not
identical), there is no division by zero here either.

2
If you save the line description in normal form at mouse down then you
can calculate the distance at mouseMove faster.  It is simply Ax + By +
C, where (x,y) is the point of interest.  This is the normalized A, B,
& C where A = cos(omega) etc., the form you mentioned in other mail.

Dar Scott

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```

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