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.

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)

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

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.

Yep, and yep.