The Distance Formula

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

The End