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Explaining The Distance Formula By: Mario Guzman Geometry per.3

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What is The Distance Formula? The Distance formula is a formula used to find the distance between to different given points on a graph. The points would be labeled as the following: (x1, y1) & (x2, y2)

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The Actual Formula The actual formula is: D= (x1 - y1)² + (x2 - y2)² “X” is the variable used for the number on the x coordinate and “Y” is the variable for the number on the y coordinate

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Example #1 Find the distance between (2,1) and (5,2). D= (2 - 5)² + (1 - 2)² D= (-3)² + (-1)² D= 9+1 D= 10 D= 3.162 x1 y1x2y2 -First write out the problem and solve the parentheses. -Then solve the squared number. -Add the two numbers. -Find the square root of the remaining number.

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Example #2 Find the distance between (3,8) & (4,6). D= (3-4)² + (8-6)² D= (-1)² + (2)² D= 1 + 4 D= 5 D= 2.236

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Example #3 Find the distance between (1,1) and (8,0) D= (1-8)² + (1-0)² D= (-7)² + (1)² D= 49 + 1 D= 50 D= 7.071

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And Now… Difficult Examples! Find the distance between (82,20) & (55,3) D= (82-55)² + (20-3)² D= (27)² + (17)² D= 729 + 289 D= 1018 D= 31.906

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Example #5 Find the distance between (0,5) & (100,67) D= (0-100)² + (5-67)² D= (-100)² + (-62)² D= 10000 + 3844 D= 13844 D= 117.660

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Larger Numbers! Find distance between (1000,200) & (23,2) D= (1000-23)² + (200-2)² D= (977)² + (198)² D= 954529 + 39204 D= 993733 D= 996.861

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Example #7 Find distance between (222,12) & (0,482) D= (222-0)² + (12-482)² D= (222)² + (-470)² D= 49284 + 220900 D= 270184 D= 519.792

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Example #8 Find distance between (1,1) & (30000,288) D= (1-30000)² + (1- 288)² D= (-29999)² + (-287)² D= 899940001 + 82369 D= 900022370 D= 30000.372 Oh…I understand now!

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Another Example! Find distance between (1000000,9000) & (300000,2001) D= (1000000-300000)² + (9000-2001)² D= (700000)² + (6999)² D= 490000000000 + 48986001 D= 490048986001 D= 700034.989

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FINAL EXAMPLE! Find distance between (0,10000000) & (1,55555) D= (0-55555)² + (10000000-1)² D= (-55555)² + (9999999)² D= 3086358025 + 99999980000001 D= 100003066358026 D= 10000153.316

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The End This Has Been A PowerPoint By: Mario Guzman

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