# Locus question #1

• Jul 31st 2010, 11:06 PM
moeyfrompunchy
Locus question #1
My question is:

Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please :)(Hi)
• Aug 1st 2010, 12:50 AM
Quote:

Originally Posted by moeyfrompunchy
My question is:

Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please :)(Hi)

In order for point P to be equidistant from the x and y-axis, it has to move along the line y=x.
• Aug 1st 2010, 09:03 AM
Soroban
Hello, moeyfrompunchy!

Did you even bother to make a sketch?

Quote:

Find the equation of the locus of a point $P(x,y)$
that moves so that it is equidistant from the $x$-axis and the $y$-axis.

Code:

|        P
B + - - - - *(x,y)
|    x    :
|        :
|        : y
|        :
|        :
----+---------+----
|        A
|

The point is $P(x,y).$

Its distance from the $x$-axis is: . $PA = y.$

Its distance from the $y$-axis is: . $PB = x.$

We want these distances to be equal: . $y \:=\:x$

How hard was that?
• Aug 1st 2010, 10:24 AM
earboth
Quote:

Originally Posted by moeyfrompunchy
My question is:

Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please :)(Hi)

1. If the point P has equal distances from the axes then you have:

$|y| = |x|$

2. If you write this equation without the absolute values you'll get as the locus l:

$l: y = x~\vee~y = -x$