Finding the Distance Between Two Points

Talk about math being applicable to real life.

GeometryCoordinate Geometry
LanguageEnglish Language
Mathematics and Statistics AssessmentPlane Geometry
Plane GeometryPlane figures (triangles, rectangles, parallelograms, trapezoids, circles, polygons)

Transcript

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.