ShmoopTube

00:06

Finding the distance between points, a la Shmoop.

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

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pasture after a night out at their favorite Indian restaurant…

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…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.

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

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

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

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

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

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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…

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… “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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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downwind.

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