Author 
Comment/Response 
Scott Danzig

10/19/09 10:37pm
What I want to do is, given an equation for a line, and an equation for a perpendicular line that passes through a point, use mathematica to come up with the equation for the distance between these points.
Given a line of Ax+By+C==0 .. I convert it to y==mx+b format:
y==(A/B)x(C/B)
So to find the perpendicular line passing through a point x0,y0, use the inverse negative slope and solve for the y intercept, C/B, where x==x0 and y==y0:
y0==(B/A)x0+(C/B) > y0(B/A)x0==(C/B)
The perpendicular line passing through a point is:
y==(B/A)x+y0(B/A)x0
So given that equation and the original line...
Ax+By+C==0
I'm trying to come up with a formulas for the coordinates of the intersection of the two lines. I tried this:
Solve[{y == (B/A) x + y0  (B/A) x0, Ax + By + C == 0}, {x,y}]
Solve::svars: Equations may not give solutions for all "solve" variables.
{{x > (B x0 + A y  A y0)/B}}
I'm wondering if someone can explain where my logic slipped up.
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