G C S E Loci Question

[kuiperbelt]

The link below shows a recreation area open to the general public.

A park bench is to be installed under the following constraints:

i. The bench is to be equidistant from point B and from point D
ii. It is to be exactly 75 metres from point C

Using a ruler and pair of compasses only.
Mark the point with an X where the bench will be situated.
All working must be shown.

https://ibb.co/422yBm7

[ClareTG0ld]

Construct a perpendicular bisector for points B and D, a circle centred on point C. I am not going to do this, but eyeballing it looks like it will end up fairly close to A.

[Atheist]

But we don't know the scale.

[Atheist]

So we don't know the radius from C.

[Atheist]

But the person who's doing this question will have it down on his paper and so presumably will be able to follow Clare's advice.

[Atheist]

I think I got there in the end. Clare explained the method.

[Atheist]

But Clare's eyeballing; I'm not so sure.....

[Prudie]

The scale is on the drawing so the radius from C is 7.5 cm

[Atheist]

Prudie; the scale is 1cm = 10m. But my computer screen doesn't let me stick a ruler up to it.
But, Clare's method is sound.

[Prudie]

I don't think we can do it on a computer screen, I assume you need the actual test paper to draw on but yes the method is fairly obvious.

[ClareTG0ld]

I'd guess that the image as shown is (more or less) actual size. As to whether I properly eyeballed a 7.5cm-radius circle, hard to say -- probably I've overestimated how large it would be.

[Prudie]

But if I open this drawing on my phone it's a completely different size to my tablet and laptop. Whatever.

[perseverer]

Is it acceptable to judge the perpendicular just by eye?

[ToraToraTora]

The exact answer isn't really relevant, the method is what counts here.

[THECORBYLOON]

If the length of one of the sides were known, it would be possible to provide an answer.

[ClareTG0ld]

// But if I open this drawing on my phone it's a completely different size to my tablet and laptop. Whatever. //

Obviously, my laptop screen represents the ideal and actual size of all images it displays, duh.

(Alternatively, I'm a moron.)

[THECORBYLOON]

I wondered if might on A4 paper and whether the four pairs of right-angle lines were in the ratios used for A sizes but they're not.

[Atheist]

I guess that we should presume that the person attempting the problem would be using a printed sheet at the right scale. The question should really have provided a proper scale as part of the diagram.

[THECORBYLOON]

There is a scale but without the measure of at least one of the sides, it's not possible to show where the "X" should be.

[Atheist]

TCL; by scale I meant a picture of a line calibrated with cm markings so that dimensions can be read whatever the variations in printing.

[Prudie]

The whole point of the question is to use a compass to make a perpendicular line half way between B and D and then draw a circle of radius 7.5 cm with its centre at C to show the point on your drawing where they cross. That's where the bench should be. It's not about calculating, it's about using a compass.