Question

10. Explain why you can use the coordinates of either point as (x, y) when finding the
distance between two points.

Answer 1

The distance formula for two points P1: (x1,y1) and P2:  (x2,y2) is:

     d = √( (x2-x1)2 + (y2-y1)2 )

 

On the number line a and b are the x-coordinates and the y-coordinates are both 0.  The points are  (a,0) and (b,0).

 

In the Distance Formula, this makes the distance:

   d = √( (x2-x1)2 )

 

Now, since the square root may have either both positive and negative roots, we write the value as:

     d = ± (x2-x1)

 

    This is either (x2-x1)  or (-(x2 - x1))

When considering distance (a measurement without a sign attached), we write the positive distance:  |x2 - x1|.