Posted by **Zach** on Monday, September 8, 2008 at 12:20am.

Show that the distance between the points (x,y) and the line Ax + By + C = 0 is:

D = (Ax + By + C) / sqrt(A^2 + B^2)

So, would you start out by multiplying sqrt (A^2 + B^2) to both sides and then it would become:

sqrt (A^2 + B^2)D = Ax + By + C

Then square both sides,

D^2(A^2 + B^2) = (Ax + By + C)^2

Then I got lost, could someone direct me through this problem? Did I start out the right way? Thanks!

- Algebra -
**drwls**, Monday, September 8, 2008 at 7:45am
Just manipulating the equation for D will not constitute a proof that it is correct. You need to derive it somehow.

Try deriving an equation for a line through (x,y) that is perpendicular to the line Ax + By +C = 0. Then compute where the two lines intersect. Call that point (x', y'). Then compute the distance between (x,y) and (x',y').

A proof can be found here:

http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html

## Answer This Question

## Related Questions

- Trig/Pre-Cal - Show that the distance between the points (x,y) and the line Ax...
- Algebra - Evaluate sqrt7x (sqrt x-7 sqrt7) Show your work. sqrt(7)*sqrt(x)-sqrt(...
- Math Help please!! - Could someone show me how to solve these problems step by ...
- Math - How do you find a square root of a number that's not a perfect square? I'...
- Algebra - Multiplying sq rts sqrt18a^7b times sqrt27a^8b^6 Jake 1214- 18 = 9 * 2...
- math,algebra,help - Directions are simplify by combining like terms. x radiacal ...
- Inequality - When I solve the inquality 2x^2 - 6 < 0, I get x < + or - ...
- algebra,math,help - Use Property 2 to simplify each of the following radical ...
- Math - 1.Find the distance between P(7, -4) and the line with equation x - 3y + ...
- Geometry - How do I find the distance between (-9,3) and (-1,-5) By using the ...

More Related Questions