Stitz-Zeager_College_Algebra_e-book

It is left to the reader to verify equation 11 for

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Unformatted text preview: Q are arranged vertically or horizontally, or describe the exact same point, we cannot use the above geometric argument to derive the distance formula. It is left to the reader to verify Equation 1.1 for these cases. Example 1.1.3. Find and simplify the distance between P (−2, 3) and Q(1, −3). Solution. (x2 − x1 )2 + (y2 − y1 )2 d= (1 − (−2))2 + (−3 − 3)2 √ 9 + 36 = √ =35 = √ So, the distance is 3 5. Example 1.1.4. Find all of the points with x-coordinate 1 which are 4 units from the point (3, 2). Solution. We shall soon see that the points we wish to find are on the line x = 1, but for now we’ll just view them as points of the form (1, y ). Visually, y 3 (3, 2) 2 1 distance is 4 units 2 3 x −1 (1, y ) −2 −3 We require that the distance from (3, 2) to (1, y ) be 4. The Distance Formula, Equation 1.1, yields 8 Relations and Functions d= (x2 − x1 )2 + (y2 − y1 )2 4= 4= (1 − 3)2 + (y − 2)2 4 + (y − 2)2 42 = 16 12 (y − 2)2 y−2 y−2 y = = = = = = 4 + (y − 2)2 2 4 + (...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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