Distance formula
Key Notes :
The distance d between the points (x1 , y1 ) and (x2 , y2 ) can be found using the distance formula:
d = √(x2-x1)2 +(y2-y1)2
Learn with an example
Find the distance between the points (10 , 8) and (2 ,2).
Write your answer as a whole number or a fully simplified radical expression. Do not round. ________ Units
To find the distance between the points (10 , 8) and (2 ,2) , use the distance formula.
The first point is (10 , 8) . So, x1 = 10 and y1=8 .
The second point is (2 ,2) . So , x2 = 2 and y2=2.
Substitute these values into the distance formula.
d = √(x2-x1)2 +(y2-y1)2
d = √(2 – 10)2 + (2 – 8)2
d = √(-8)2 + (-6)2
d = √64 + 36
d = √100
d = 10
The distance between (10 , 8) and (2 ,2) is 10 units.
Find the distance between the points (6 , 7) and (10 ,4).
Write your answer as a whole number or a fully simplified radical expression. Do not round. ________ Units
To find the distance between the points (6 , 7) and (10 ,4) , use the distance formula.
The first point is (10 , 8) . So, x1 = 6 and y1=7 .
The second point is (2 ,2) . So , x2 = 10 and y2=4.
Substitute these values into the distance formula.
d = √(x2-x1)2 +(y2-y1)2
d = √(10 – 6)2 + (4 – 7)2
d = √(4)2 + (-3)2
d = √16 + 9
d = √25
d = 5
The distance between (6 , 7) and (10 ,4) is 5 units.
Find the distance between the points (5 , 0) and (8 ,4).
Write your answer as a whole number or a fully simplified radical expression. Do not round. ________ Units
To find the distance between the points (5 , 0) and (8 ,4) , use the distance formula.
The first point is (5 , 0) . So, x1 = 5 and y1=0 .
The second point is (8 ,4) . So , x2 = 8 and y2=4.
Substitute these values into the distance formula.
d = √(x2-x1)2 +(y2-y1)2
d = √(8 – 5)2 + (4 – 0)2
d = √(3)2 + (4)2
d = √9 + 16
d = √25
d = 5
The distance between (5 , 0) and (8 ,4) is 5 units.
let’s practice!
