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i needs help

 

what is the distance formula?

TheBestAquamarine  Aug 3, 2017

Best Answer 

 #2
avatar+5576 
+3

Let's look at the points  (4, 5)  and  (6, 2)  for example.

We can make a right triangle out of these points like this...

 

Notice that side  c  is the distance between the two points.

 

And..we can find the length of side  c  using the Pythagorean theorem, which says..

 

    a2    +     b2     =  c2

                                                       The length of side  a  =  5 - 2  =  3

(5 - 2)2 +     b2     =  c2

                                                       The length of side  b  =  6 - 4  =  2

(5 - 2)2 + (6 - 4)2  =  c2

                                                       Take the positive square root of both sides.

\(\sqrt{(5-2)^2+(6-4)^2}=c\)

 

And this is where the distance formula comes from. It says..

 

\(\text{distance}=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

 

And, as CPhill noted, the order of subtraction within the parenthesees doesn't matter.

hectictar  Aug 3, 2017
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2+0 Answers

 #1
avatar+79894 
+2

 

Suppose that we have two points (x1, y1)  and (x2, y2)

 

The distance between these is just

 

sqrt [  (  x2 - x1)^2 + ( y2 - y1)^2 ]   ..  actually....the order of subtraction is immaterial...we could subtract (x1 - x2 )  or (y1 - y2) or both in this order

 

Example.....distance between (5,3)  and (8, 2)

 

sqrt [  ( 5 - 8)^2 + (3 - 2)^2 ]   =  sqrt [ (-3)^2 + 1^2 ]  =  sqrt [ 9 + 1 ] =  sqrt (10)  units ≈  3.16 units

 

 

cool cool cool

CPhill  Aug 3, 2017
edited by CPhill  Aug 3, 2017
edited by CPhill  Aug 3, 2017
edited by CPhill  Aug 3, 2017
 #2
avatar+5576 
+3
Best Answer

Let's look at the points  (4, 5)  and  (6, 2)  for example.

We can make a right triangle out of these points like this...

 

Notice that side  c  is the distance between the two points.

 

And..we can find the length of side  c  using the Pythagorean theorem, which says..

 

    a2    +     b2     =  c2

                                                       The length of side  a  =  5 - 2  =  3

(5 - 2)2 +     b2     =  c2

                                                       The length of side  b  =  6 - 4  =  2

(5 - 2)2 + (6 - 4)2  =  c2

                                                       Take the positive square root of both sides.

\(\sqrt{(5-2)^2+(6-4)^2}=c\)

 

And this is where the distance formula comes from. It says..

 

\(\text{distance}=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

 

And, as CPhill noted, the order of subtraction within the parenthesees doesn't matter.

hectictar  Aug 3, 2017

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