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#1 2007-05-24 23:58:42

Identity
Member
Registered: 2007-04-18
Posts: 934

Similarity q.

This was the final question on the test which we had on similarity and congruency. Baaah! It was worth 5 marks, and I couldn't do it, and the test was out of 30! mad I must say the questions on the test were much harder than I anticipated, but oh well, the harder the problems the more I learn I suppose!

Here 'tis (the diagram was not drawn on the paper):

thanks again

Last edited by Identity (2007-05-24 23:59:24)

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#2 2007-05-25 00:53:34

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Similarity q.

PolesApart.jpg

So the answer to the question is 1.6 cm.

BTW I entitled the image “Poles Apart”. tongue

Last edited by JaneFairfax (2007-05-25 00:58:34)

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#3 2007-05-26 17:22:10

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Similarity q.

smile I always have a tendency to understimate the value of abstracting what you see as geometry into algebraic equations. What I found interesting is that although you have 3 variables and 2 equations, you eventually come out with a numerical answer for x. Is that the case often?

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#4 2007-05-26 18:12:24

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Similarity q.

In this particular case, x happens not to depend on the distance between the two poles. You can move the poles closer to or further away from each other, and the point of intersection of the two “diagonal” lines will always be the same constant height above the ground.

I think I’ve seen a question similar to this before in some problem on optics. You are given a system of lenses or mirrors and a light source, and you are supposed to show that the height of the image is independent of the relative distance between the light source and the lens/mirror system.

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