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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)
The Actual Formula
• The actual formula is: D= (x1 – x2)² + (y1 - 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
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 y1 x2 y2
-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.
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
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
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
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
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
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
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!
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