Question

Joe and Tim observed two points, P, and Q, on a number line.

Joe said that the absolute values of the numbers represented by the two points are different.

Tim said that the absolute values of the numbers represented by the two points are the same.

Which of the following explains who is correct? How did you get your answer?

Joe, because the points have different signs
Tim, because each point is fraction 3 over 8 unit away from 0
Tim, because the distance between the points is fraction 3 over 8 unit
Joe, because the points are at different locations

Answer 1

Answer: Choice B) Tim is correct.
Each point is 3/8 of a unit away from 0

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The point 3/8 is 3/8 of a unit away from 0
The point -3/8 is also 3/8 of a unit away from 0
The absolute value of a negative number is simply the positive version of that number. So |-3/8| = 3/8. Negative distances do not make sense which is why this happens.

Answer 2

Tim, because each point is fraction 3 over 8 unit away from 0

Explanation:

The absolute value of a number can be defined by the distance from that point to the origin.

That said, for every number of the number line there is another whose distance to the origin is the same. it is a number with the same module and different sign, what we know as the opposite

In this case P= -3/8 = -Q and modP =mod-P=modQ + mod -Q = 3/8