# Finding a point a certain distance from a line.

• Oct 14th 2008, 01:34 PM
BenBart
Finding a point a certain distance from a line.
http://benbart.com/images/math.jpg
(I just want to note that I made up this problem. I'm not trying to cheat on a test or anything.)
• Oct 14th 2008, 01:44 PM
Peritus
$\displaystyle \sqrt {(x - 1)^2 + (y - 1)^2 } = 2$
• Oct 14th 2008, 01:44 PM
icemanfan
The point satisfies $\displaystyle \sqrt{(x-2)^2 + (y-1)^2} = 2$ and $\displaystyle y = 2x - 3$.

Substitution yields:
$\displaystyle \sqrt{(x-2)^2 + (2x - 4)^2} = 2$

$\displaystyle \sqrt{(x-2)^2 + 4(x-2)^2} = 2$

$\displaystyle 5(x-2)^2 = 4$

$\displaystyle (x-2)^2 = \frac{4}{5}$

$\displaystyle x-2 = \sqrt{\frac{4}{5}}$

$\displaystyle x = \sqrt{\frac{4}{5}} + 2$

Now you plug x back into the line equation to find y.
• Oct 14th 2008, 03:58 PM
BenBart
Clarity
I just want to clarify that what I'm looking for is the point where that circle is intersecting the line. I'm not looking to solve for the X coordinate.

So I'm not looking for that answer that's around (4,5) I'm looking for the one that's around (2.9, 2.8)ish – I thought I would need pi.

If this is in fact the correct solution then I guess I need a little help figuring out what the 1's and 2's represent.
• Oct 14th 2008, 06:49 PM
BenBart
How to solve.
Problems get bumped fairly quickly in this section. Is there a more appropriate place to post this? Geometry, pre-calc?