# 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 \$\displaystyle P(x,y)\$
that moves so that it is equidistant from the \$\displaystyle x\$-axis and the \$\displaystyle y\$-axis.

Code:

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

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

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

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

We want these distances to be equal: .\$\displaystyle 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:

\$\displaystyle |y| = |x|\$

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

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