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Finding the Distance Between Two Points

Finding the Distance Between Two Points. (-6,4). (1,4). -7. -2. -1. 1. 3. 5. 7. -6. -5. -4. -3. 0. 4. 6. 8. 2. Let's find the distance between two points. 7 units apart. 8. 7. 6. So the distance from (-6,4) to (1,4) is 7. 5. 4. 3. 2. 1. -2. -3. -4. -5. -6. -7.

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Finding the Distance Between Two Points

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  1. Finding the Distance Between Two Points

  2. (-6,4) (1,4) -7 -2 -1 1 3 5 7 -6 -5 -4 -3 0 4 6 8 2 Let's find the distance between two points. 7 units apart 8 7 6 So the distance from (-6,4) to (1,4) is 7. 5 4 3 2 1 -2 -3 -4 -5 -6 -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.

  3. What coordinate will be the same if the points are located vertically from each other? (-6,4) -7 -2 -1 1 3 5 7 -6 -5 -4 -3 (-6,-3) 0 4 6 8 2 8 7 6 5 4 3 2 7 units apart 1 -2 -3 So the distance from (-6,4) to (-6,-3) is 7. -4 -5 -6 -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.

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

  5. 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. (x2,y2) (x1,y1) -7 -2 -1 1 3 5 7 -6 -5 -4 -3 0 4 6 8 2 This is called the distance formula 8 Let's start by finding the distance from (x1,y1) to (x2,y2) 7 6 5 ? 4 y2 – y1 3 2 1 x2 - x1 -2 -3 Again the Pythagorean Theorem will help us find the hypotenuse -4 -5 -6 -7 Solving for c gives us: Let's add some lines and make a right triangle.

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

  7. 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. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

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