# WitCH 9: A Distant Hope

This WitCH (as is the accompanying PoSWW) is an exercise and solution from Cambridge’s Mathematical Methods Units 1 and 2, and is courtesy of the Evil Mathologer. (A reminder that WitCH 2, WitCH3, Witch 7 and WitCH 8 are still open for business.)

## Update

As Number 8 and Potii pointed out, notation of the form AB is amtriguous, referring in turn to the line through A and B, the segment from A to B and the distance from A to B. (This lazy lack of definition appears to be systemic in the textbook.) And, as Potii pointed out, there’s nothing stopping A being the same point as C.

And, the typesetting sucks.

And, “therefore” dots suck.

## 4 Replies to “WitCH 9: A Distant Hope”

1. Number 8 says:

AB=BC is really ambiguous. I assume they mean the length of line segment AB and BC. Otherwise, it is impossible for the two to be equal (vectors not being in Methods)

1. marty says:

Yes, though it’s worse than that. (And there’s more.)

2. Potii says:

They didn’t say point C cannot be the same point as A. This still satisfies AB = BC.

BD is a segment, so the equation of it needs to have restrictions on the domain. Though their answer is for the equation of the line that passes through points B and D.

1. marty says:

Yep, and yep.

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