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

[perseverer]

Prudie - use the ruler to draw the perpendicular line ..... and the compasses to draw the circle...

[THECORBYLOON]

PRUDIE, how do you draw a circle with a radius of 7.5cm without using a ruler to measure that distance?

[Prudie]

The ruler for the BD line yes but then the compass to find the 2 points to join that will cut BD in half perpendicular. That satisfies the equidistant locus part. Where the circle then cuts that line is where the bench goes.

[Prudie]

Lordy. I never said you didn't, that bit is surely a given. You put the compass point on C having opened your compass against a ruler so your pencil is on 7.5 and draw an arc.
I wouldn't have added anything more at all if you hadn't started talking about angles and calculations.

[lankeela]

Are you not supposed to have learnt this yourself if you are doing an exam? What is the point of asking for the answer?

[zebo]

I measured the sides and guestimated the angles then drew it to scale, it places the bench about 10 m along AD and about 2m inside the quad.

[zebo]

Scrub that , it's about 10m fronm and 2m in from line AB, I labelled mine incorrectly.

[ZebuSanctuary]

Unless more information about the scale is given, this problem does not lend itself to being solved online. The scale in question is only meaningful to a hard copy.

Had the diagram been accompanied by a standard guage (as seen on a map), a straight line of fixed length eg. _____ = 1 cm then this would have adjusted itself automatically in direct proportion to the dimensions of the shape, whether viewed on tablet, PC, i-phone etc

That said, for the benefit of the student, the link below will hopefully provide an insight into how the problem should be treated in working towards a solution.

Note the position of X cannot be ascertained with any great accuracy due to limitations on scale. However the student should at least recognise the techniques used in the method I have outlined.

https://ibb.co/KbtgTKg

[zebo]

Zebu, if we're related I could probably be your mother looking at our joining dates, mine is about 6 years before the on site info implies, I changed my email address and the site wouldn't let me change it without sending a notification to the now defunct address!