locus (1 Viewer)

[205021]

The distance of a point from the line x=4 is equal to its distance from y=1. Find the equation of the locus.

I know there are two answers, I just keep ending up with y + x = 5 and not getting y - x = 3. How do I solve this properly?

 

[jet]

This should really be in the Maths forums but anyway,
Let the arbitrary point be P, and let point M lie on x = 4, and N lie on y = 1.
We take PM, realising that this is the perpendicular distance to x - 4 = 0
PM = |(x) - 4|/1
PM = |x - 4|
Also, PN is the perp. distance to y = 1
PN = |(y) - 1|/1
PN = |y - 1|
Now, we make the two equal, |x - 4| = |y - 1|
There will be four solutions, as we have to consider that both sides can be positive or negative inside the absolute values
So,
x - 4 = y - 1, x - y = 3
x - 4 = -(y - 1), x + y = 5
-(x - 4) = y - 1, x + y = 5
-(x - 4) = -(y - 1), x - y = 3

 

[205021]

cheers mate, i knew it was something simple just couldnt work it out myself. Yeah, I meant to put it in the maths forums. Woops

Thanks