On the PSAT and SAT tests is it ever worth it to just try using their diagram even though it says it's not drawn to scale, I mean just to save time instead of going through the trouble of redrawing it from scratch the way a lot of the books say you should? I mean, even if they are not perfect, can't some of them be close enough to give you the idea?
High School Junior
It is NEVER a good idea to rely even a drop on such a drawing. Remember, unlike tests and quizzes given in school, often composed by a teacher who has a busy family life and plenty of other things going on his/her mind other than that particular test, the SAT people have the resources and time and incentive to hire teams of artists to construct their diagrams to perfection. It helps to understand that -- although the authors of the SAT may be mean and tricky, they are NOT careless or lazy when it comes to the way they make their test. Every word is there for a reason, even if at the time it is difficult to figure out what that reason might be.
When a figure is accompanied by the words 'not drawn to scale' or some variant of that, it is not because the authors didn't have the time or resources to construct it perfectly. NO. No. NO, that is not what's going on.
What is going on is this: The drawing is there to mislead you. Look away from it, look off into the distance and forget that distorted trick of a 'diagram'. (Just as vampires often turn away in fear from a cross in many of the old vampire movies). That drawing is your enemy. Either redraw the diagram based upon what info you can glean from the words of the question, or use some other method. BUT that drawing is BAD NEWS. You cannot expect to get to any reasonable answer relying on it. (A corollary though is this: if it doesn't say that, you CAN rely on it as though it was gold.)
Hope this helps,