The other day in Math we were finding the distance between two points. My teacher taught us some confusing formula (I don't even remember it). I graphed the points are realized something. Say the points were (3,2) and (-1, 4). Graph them like so:



Then you are going to connect them like this:



Notice something? If I do this....



You get a right triangle! The line that you need to find the distance of is the hypotenuse! Simply find the length of the legs....



Then do Pythagorean theorem....



And you get your distance! It is so much easier and quicker than using the distance formula!

My teacher hates me now because I taught it to the whole class and they use it instead of the formula she taught.

I am pretty sure that I did not invent this method, but I did figure it out by myself. I hope this is useful, and I apologize if your teachers taught this to you already and I just wasted your time.

Good job tgags.
IIRC, my teacher started by teaching the long complicated method then eventually showed us this method as well.

 I gotta say that you are adorable and that you're teachers are awful.

You basically derived the distance formula. LOL That is exactly where the distance formula comes from. I'm super impressed! Great job!

EDIT:  Didn't mean to summon you vanelan, sorry . XD

I knew about this...just saying. But it is easier than the distance formula and makes life SO much simpler. It's impressive that you came up with that too. Nice job.

Singelli : Indeed, they are awful. Well, just my math teacher. My other teachers are great.

Haha thanks! Math never really makes any sense to me, part of that is probably because my last three math teachers have been absolutely terrible, but for some reason this just clicked and it actually made sense!

tgags123 :  Well this is one of  the reasons I'm NOT a fan of memorization in math.  Too many teachers emphasize things like... memorizing the distance formula... instead of getting kids to simply understand the whys and hows.  Just think... if you knew the reasons behind more formulas, wouldn't they be easier to understand?  Plus, if you forgot the formula... it wouldn't be a big deal, because you'd know how to work the problem regardless.... like you did here.  

A user of this : It is a radical symbol, meaning square root. The answer would just be radical 20, but if you simplified it down you would get 4,47213........

tgags123 : Oh, I see. Well, back to remembering square roots. You'd combine both answers together right? (I have no experience in using radicals. lol sorry)

Actually, our teacher taught us to do it this way. Yay for skipping long formulas! And congrats on figuring it out yourself.

A user of this : What do you mean? You know how to do Pythagorean theorem (man that is hard to spell) right? All you are doing is pythagorean theorem, only it doesn't come out to a even number, it comes out to a radical. The answer would be √20.

My question is what formula was your teacher giving you? That method is what I have always been taught. Why make it more complicated?

tgags123 : I guess I can look it up. I don't anything on that yet. As soon as I get new homeschool stuff it should be in there. But your method seems simple enough.

rcarter2 : I don't even remember since I do it this way. It was something along these lines:

Distance= √(x-x) + (y-y)

I am not even sure if I did that right, it was similar to that. It is really a pain if they ask you to prove that it is a parallelogram and you need to do that for every side!

tgags123 :

You'd need to square both (x-x) and (y-y). And to make it easy to realize, look at how you found the lengths for sides A and B on your triangle. That's the same thing, although you may notice that either (x-x) or (y-y) will be negative in the example you gave. That won't matter, because a negative number squared is always positive.

So when you use the pythagorean theorem, you're just substituting A for (x-x) and B for (y-y).