Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 321

Loci. Stadiums (stadia?)

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, the 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 the line, 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, doesn’t actually cover THE LOCUS OF ALL POINTS 3CM FROM THE LINE?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Loci. Stadiums (stadia?)

It is imprecise. As it stands the locus should include points inside the stadium. That covers the point you're making.

If they only wanted the lines and semicircles it should specify the shortest distance.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Loci. Stadiums (stadia?)

Thanks, Bob.

How would that be worded?

"Draw the locus of all points..."

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Loci. Stadiums (stadia?)

Whose shortest distance from the given line segment is 3cm

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob