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Distance Formula

Okay, you learned some stuff back in algebra that is going to come in VERY handy right now. Yep, it is! Do you remember the ol' Pythagorean Theorem? A-ha! Well, here's your chance to use it again. And, believe it or not, it is NOT just used in math classes either!

So, just how in the heck is this formula important in distance? Funny you should ask. You can use the Pythagorean Theorem to find the distance between two points in a coordinate plane. Let's take a look at exactly what this means visually.

distance

Here is a right triangle on a coordinate grid. You can easily tell the distance from point A to point C (the base) and the distance from point B to point C (the height).

m AB = 5
m BC = 6
 

If you wanted to find the distance from point A to point B, you can use the Pythagorean Theorem. a2 + b2 = c2

Let's try it!

a = 5 and b = 6 so just substitute the numbers for the variables in the formula.

52 + 62 = c2
25 + 36 = c2
61 = c2
√61 = c
7.8 ≈ c

The Distance Formula

"There's got to be another way to find the distance!" you exclaim. Yep, there IS a formula (of course there is!). So, if you want to use a formula instead, you can do so!

The formula requires that you know the coordinate points. If you have the two coordinates, then you can figure out the distance by simply substituting those values!

distance1

Coordinates for the two points are:

A (2, 1)
B (7, 7)

Let's just substitute the values and see what happens.

distance2

Do the numbers look familiar? I bet they do!

Why? Hmmm…could it be because they look an awful lot like what we did with the Pythagorean Theorem? A-ha!

©2016 Sherry Skipper Spurgeon for Geometry Bugs Me

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