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Collinearity a la shmoop for the past 27 years Dr. Frankenstein [Dr Frankenstein appears]

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has been slaving away over his creation an eight-foot-tall reanimated corpse

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named Manny one day Manny took a stroll outside the [Manny walking outside]

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castle and ran into some Transylvanian villagers rather than being charmed by

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Manny they were immediately frightened by his size and decaying skin some

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people are just too into appearances if you ask us the villagers started chasing [Villagers chase Manny away]

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Manny who ran back toward the castle the distance from the castle to the

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villagers is four miles and the villagers are one mile away from Manny

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how far away is Manny from the castle well let's look at these points on ye

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olde map of Transylvania let's start with the castle we know that the angry [Castle appears on a map]

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villagers are four miles away and that Manny is one mile away from them looks

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pretty easy doesn't it but what if the map looked like this or this well right

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now we don't have enough information to answer the question because we don't

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know if the points are collinear when three or more points are collinear a

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single line can be drawn through all of them the word between also indicates

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collinearity and position so if we know that many is between the castle and the [Manny stood between castle and villagers on a map]

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mob of angry villagers we know that they're all collinear with Manny in the

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middle and the castle and the villagers on either side of it if that's the case

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we can solve for the distance between the castle and Manny by subtracting the

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distance between Manny and the villagers from the distance between the villagers

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and the castle piece of cake the four miles minus one mile is three miles that

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means Manny is three miles away from Dr. Frankenstein's castle and with that

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stride they'll make it to safety for sure... As for Dr. Frankenstein he'll need [Manny runs into castle]

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some luck when dealing with those angry villagers

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