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Geometry Videos 251 videos

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Finding the Distance Between Two Points 2065 Views


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Description:

Talk about math being applicable to real life.

Language:
English Language

Transcript

00:06

Finding the distance between points, a la Shmoop.

00:10

Meet Bossy. Any time Bossy and company come back to the

00:13

pasture after a night out at their favorite Indian restaurant…

00:16

…Bossy sets up camp at her chosen spot… … and orders the other cows to move as far

00:21

away from her as possible. Honestly, it’s for their own good.

00:24

If we imagine the cows’ situation on a coordinate plane…

00:27

…it might look something like this. Plus, it’s much more appetizing to view

00:31

it as a graph than to see the actual field. Trust us on this one.  

00:36

So which cow is going to be in Bossy’s good graces?

00:39

In other words, which cow is farthest away from Bossy, and her… leftovers?

00:44

To figure it out, we’re going to have to rely on one of those coordinate geometry formulas

00:48

we love so much. In this case, we want to find the distance

00:51

between two foul-smelling points, so we’ll need…

00:56

… “distance equals the square root of x1 minus x2 squared, plus y1 minus y2 squared.”

01:05

We may also need some nose plugs. Ever heard of a cow pie?

01:09

Well, we can find the distance between Bossy and each of the five cows by substituting

01:14

“x2, y2 equals zero, zero” into the distance formula…

01:21

…because Bossy is at the origin, or “zero, zero.”

01:26

Basically, it's like “x2, y2” doesn't even exist.

01:31

Then it’s just a matter of plugging in each cow’s coordinates.

01:36

Which would be easier if each of them was equipped with a GPS.

01:41

The coordinates of point A are (-2,3).  So when we plug those coordinates into our formula,

01:49

it gives us the distance from that cow to Bossy which equals… the square root of 13.

01:58

The coordinates of point B are (2, 2)… making the distance the square root of 8.

02:12

Point C is (-3, -3), which gives us the square root of 18…

02:20

…Point D at (0, -4) gives us 4… …and point E at (2, -1) gives us the square

02:36

root of 5. The largest of those is the square root of

02:41

18… or three square root of two… …which means that Betty, the cow at Point

02:49

C, is the farthest from Bossy. Lucky Betty. Let’s just hope she’s not

02:54

downwind.

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