How do I solve this locus problem?

Question

I have this problem:

Given line L, find the locus of points no more than 4 inches from line L.

I am thinking the answer is a line on either side of line L that is 4 inches away from it, but the question says "No more than 4 inches" so would it be something else?

Would the answer be two parallel lines that are 4 inches away from line L and its interior points? Is there such thing?

Answer 1

A locus is usually a line figure and not a zone.

In the question given, if the line is having a fixed length, it will be all points on the perimeter and inside of a figure that is two parallel lines 4 inches away from the line segment and bounded by two semicircles radius 4 inches joining the parallel lines.



In 3D this will be a solid of rotation of the 2D figure. All points on the surface and inside the figure will be included.



Curiously all points on the original line will also satisfy the condition!

Answer 2

I think the answer would be a Bubble looking kind of L 4 inches around L (an L rounded at the top and to the right pointing line). Do you get the picture?



Then shade in everything inside that large L. That's your locus.

Answer 3

if u will look in a 3D, it will come out to be a solid cylinder i.e.<4 inches

4 inches becomes the radius



if you looking in 2 D, less than 4 inches, will give u the entire region, with the line in the between.