Is absolute value |5| and |-5| in same or opposite directions from zero

1 answer

The absolute value of both \( |5| \) and \( |-5| \) is the same, which is 5. However, when you consider the direction from zero on a number line:

  • \( |5| \) corresponds to the point 5, which is 5 units to the right of zero.
  • \( |-5| \) also corresponds to the point 5, because the absolute value measures distance without regard to direction.

So, both \( |5| \) and \( |-5| \) are in the same direction from zero, towards the positive side of the number line. In terms of their values (magnitude), they are the same, but they originate from different original numbers (5 and -5) which have opposite signs. However, in the context of absolute value, they represent the same distance from zero.