Geometry - Locus?

Question

On my homework it asks things like "describe the locus of all points in space that are 2cm above a plain" or "describe the locus of all points that are 5cm from line p".

Please give me your best child-definition (simple) on what a Locus is. Thank you.

Answer 1

The word locus is from Latin and means place or location.
-
Here locus mean a set of all points having some properties.
-
For example, locus of all points having the same distance from a fixed point is a circle.
-
Or your examples:

"describe the locus of all points in space that are 2 cm above a plain" - locus of such points is just another plain, parallel with original plain, but 2 cm above it
-
"describe the locus of all points that are 5 cm from line p" - it is an endless cylinder surrounding the line p and having a radius 5 cm
-
Here is a simple web page:
http://regentsprep.org/Regents/math/locuspt/What.htm
-
In wikipedia I found another one:
http://en.wikipedia.org/wiki/Locus_%28mathematics%29
-
An ellipse is a locus of ... look here ->
http://mathworld.wolfram.com/Ellipse.html
-
Good luck.
-