Locus of all points -- Imprecise question?

[paulb203]

TL;DR Summary: When asked to show the LOCUS OF ALL POINTS how precise should the questioner be?

I was asked to draw THE LOCUS OF ALL POINTS 3cm from a line.

I measured 3cm above and below the line, and drew two parallel lines there. Then drew two semi-circles with radii 3cm out from either end of the line to complete the locus (a shape which Google tells me is a stadium).

But is the question imprecise?

Regards the lines above and below the line; shouldn’t it specify that the distance of 3cm is perpendicular?
There are many points 3cm from the line INSIDE THE STADIUM, no? (If you measure at an angle).
E.g. Draw a 3cm line perpendicular to, and north of, the line. Then from the base of that line, draw another 3cm line at an angle of 45 degrees to the line. The point where this new line ends will be more than 1cm inside the stadium.

Doesn’t that mean that your original shape, your stadium in this case, doesn’t actually cover THE LOCUS OF ALL POINTS 3CM FROM THE LINE?

 

[BvU]

I was asked to draw THE LOCUS OF ALL POINTS 3cm from a line.

That generally means perpendicular distance (a line segment of 3 cm fits between the point and the line)

I don't think a mathematical line is of finite length ... so you might ask yourself what the definition is in the context of your exercise.

$\$

 

[Mark44]

I agree with @BvU that distance means the perpendicular distance, and that a mathematical line has no endpoints. The intended solution of the problem is two parallel lines on either side of the given line, and 3 cm. away from it.