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Student Support Forum: 'A bit confused with solving equations' topicStudent Support Forum > General > "A bit confused with solving equations"

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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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