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|.