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Transcript 
Explaining The Distance
Formula
By: Mario Guzman
Geometry per.3
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 - 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
Example #1
• Find the distance between (2,1) and (5,2).
x1 y1
•
•
•
•
•
D=
(2 - 5)² + (1 - 2)²
D=
(-3)² + (-1)²
D=
9+1
D= 10
D= 3.162
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
Oh…I
understand
D= (-29999)² + (-287)²
now!
D= 899940001 + 82369
D= 900022370
D= 30000.372
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
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
The
End
This Has Been A
PowerPoint By:
Mario Guzman
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