e668b1106d3390d8d6693d46d7b744d9

Falling In Love with the Distance Formula

e668b1106d3390d8d6693d46d7b744d9

I know it seems like there’s a million different things you have to memorize for math class and the distance formula is just another one.  Here’s the secret about the distance formula though… it’s not some new thing to learn… you already know it!  Don’t believe me?  Check this out.

Remember the Pythagorean Theorem?  Of course you do! Hmmmm. Okay maybe you don’t.  Here it is: in any right triangle with legs of length a, b and hypotenuse c, a2 + b2 = c2. Okay, now if we solve this equation for c, we get

distance1
Right? Right.  Okay, now think about this here triangle for a sec:

749px-Distance_Formula.svg

The length of the hypotenuse is d, which is also the distance between the points (x1,y1) and (x2,y2).  The length of the legs of this triangle are x2-x1 and y2-y1.  So let’s use this information and substitute these values into the Pythagorean Theorem.  The hypotenuse is d=c, and the legs are a=x2-x1 and b=y2-y1.

distance1

distance2

Oh my goodness! It’s amazing! As you can see, the distance formula is just the Pythagorean Theorem in disguise!  So go ahead and fall in love… all over again.

For more help, check out our study video for the distance formula.

Loading Facebook Comments ...
Loading Disqus Comments ...

Leave A Comment?