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DISTANCE BETWEEN TWO POINTS Done by : Darrel Chua (03) Sean Heng (06)

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VIDEO FOR UNDERSTANDING

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CONVENTIONAL WAY We would measure the length then scale the length Use a ruler!!

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THE FORMULA

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WHY? The formula, derived from the Pythagoras theorem states that square a and square b, add them together, and square root them, you get the length of c, hypotenuse. 1.1

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(CONTINUED…) In this case we have a red line. The rise is shown by the line marked y, and the run is marked by the line x. This corresponds to the lines a and b from the previous picture (1.1). Now, we have the red slanted line, which corresponds to the hypotenuse c in the previous picture(1.1). 1.2

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RUN/RISE

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TO FIND DISTANCE… First, we square the run, which is x2 − x1. Then we square the rise, which is y2 − y1,. We then add these two values together. We should get this: (x2 − x1)squared +( y2 − y1)squared As we have seen, the two values are equal to the hypotenuse squared. Therefore we have to square root the equation to get the final product:

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IS THERE SUCH A THING AS FINDING THE DISTANCE OF A LINE? (VERSUS, FINDING THE DISTANCE OF A LINE SEGMENT). There is no such thing as finding the distance of a line. A "line" is actually considered to be abstract. This is because the "line" is considered to be infinite and continuous in both directions. It is impossible to measure an infinite distance. However, it is possible to find the distance of a line segment. This is because a line segment is actually the distance between two points of the infinite line.

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COMIC!!

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SOURCE http://www.icoachmath.com/SiteMap/Run.html http://www.icoachmath.com/SiteMap/Run.html http://www.1728.com/distance.htm http://www.1728.com/distance.htm http://www.stripgenerator.com http://www.stripgenerator.com http://www.youtube.com http://www.youtube.com http://www.purplemath.com/modules/distform.htm http://www.purplemath.com/modules/distform.htm Slide 5,6,8 info from Timothy and Liang Hao http://www.online-convert.com/result/b5f4dae17d8e42b46297a28de71f1d73 http://www.online-convert.com/result/b5f4dae17d8e42b46297a28de71f1d73

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Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x 2 + 55 =

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