why is the absolute value of a difference between two points the distance between the two points?

Question

anonymous · Answer

Absolute value is defined to be the distance for that number to zero. Hope this helps.

anonymous · Answer

say you have to graph |Z-1|=2 why can you interpret that as set of points Z such that its distance from 1+0i is 2?

anonymous · Answer

|dw:1350906322727:dw| the distance on the number line from 2 to 0 is 2. the distance from -2 to 0 is also 2. because there is no such thing as a negative distance.

anonymous · Answer

|dw:1350906546004:dw| *** sorry wrong drawing lol

anonymous · Answer

|Z-1|=2 so for that why can you say its points where distance from 1,0? like if you have |Z1-Z2| distance of Z1 from Z2??

unklerhaukus · Answer

because a distance is always positive