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2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 Let's find the distance between two points. So the distance from (-6,4) to (1,4) is 7. If the points are located horizontally from each other, the y coordinates will be the same. You can look to see how far apart the x coordinates are. (1,4)(-6,4) 7 units apart

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2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 What coordinate will be the same if the points are located vertically from each other? So the distance from (-6,4) to (-6,-3) is 7. If the points are located vertically from each other, the x coordinates will be the same. You can look to see how far apart the y coordinates are. (-6,-3)(-6,4) 7 units apart

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2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 But what are we going to do if the points are not located either horizontally or vertically to find the distance between them? Let's add some lines and make a right triangle. This triangle measures 4 units by 3 units on the sides. If we find the hypotenuse, we'll have the distance from (0,0) to (4,3) Let's start by finding the distance from (0,0) to (4,3) ? 4 3 The Pythagorean Theorem will help us find the hypotenuse 5 So the distance between (0,0) and (4,3) is 5 units.

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2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 Now let's generalize this method to come up with a formula so we don't have to make a graph and triangle every time. Let's add some lines and make a right triangle. Solving for c gives us: Let's start by finding the distance from (x 1,y 1 ) to (x2,y2)(x2,y2) ? x 2 - x 1 y 2 – y 1 Again the Pythagorean Theorem will help us find the hypotenuse (x 2,y 2 ) (x1,y1)(x1,y1) This is called the distance formula

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Let's use it to find the distance between (3, -5) and (-1,4) (x1,y1)(x1,y1)(x2,y2)(x2,y2) 3 -5 4 CAUTION! You must do the brackets first then powers (square the numbers) and then add together BEFORE you can square root Don't forget the order of operations! means approximately equal to found with a calculator Plug these values in the distance formula

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Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

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