| What else could we do with two points? | ||
| We could find the distance between them! | ||
| Let's find the distance between | ||
| our old friends from the last page ... | ||
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| So how do we do it? | ||
| We use something called the Pythagorean Theorem | ||
| (What a name, eh?) | ||
| Anyway, it works when you have a triangle | ||
| with a 90 degree angle (called a right triangle). | ||
| The deal is, in a right triangle, | ||
| if you take the lengths of the two shorter sides | ||
| multiply them times themselves and add that together | ||
| you get the same answer as you do | ||
| when you take the longest side of the triangle | ||
| and multiply it times itself. | ||
| In math talk ... | ||
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| Oh yeah?, | ||
| Well I didn't see any triangles on the graph. | ||
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Well then you're not looking hard enough. |
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| It's there ... really. | ||
| One of the lines of the triangle, | ||
| is the line between the two points. | ||
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| and a line that runs straight down | ||
| from the point on the right ... | ||
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| and a line that runs straight across | ||
| from the point on the left. | ||
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| If you put them together, you get ... | ||
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| Since one of these last two lines runs exactly up and down | ||
| and the other one runs exactly left and right | ||
| where they meet, they make a 90 degree angle. | ||
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| We also know that the point where the two lines meet | ||
| has the X value of the point on the right | ||
| and the Y value of the point on the left. | ||
| Study the picture until you understand why. | ||
| Now we can find the lengths of the two shorter sides. | ||
| The one that runs from left to right | ||
| goes from the point (1,2) to the point (5,2) | ||
| For both of these points, Y = 2. | ||
| That means the distance is the difference | ||
| between the X coordinates ... | ||
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| We can use this trick to find the distance | ||
| between the two points on the right side. | ||
| The X values of these two points are both 5, | ||
| only the Y values are different. | ||
| The distance between these points is that difference. | ||
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| Now we know the lengths we need | ||
| to use that Pythagorean Theorem thing. | ||
| It will let us figure out the length | ||
| of the long side of the triangle. | ||
| Which just happens to be the distance | ||
| between the two points! | ||
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| This time, we don't have to worry about that +/- thing | ||
| that you usually get with a root. | ||
| That's because we're talking about a distance here. | ||
| And this distance is not going to be negative number. | ||
| So the distance between the points (1,2) and (5,3) | ||
| is about 4.124. | ||
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copyright 2005 Bruce Kirkpatrick |
