Barbara plotted an elevation below sea level on a number line and labeled it A. She plotted Point B above 0, a distance that is exactly as far from 0 as Point A is. Explain what you know about Point B.

Answer 1

Since Point A represents an elevation below sea level, it will have a negative value on the number line. Let's denote the value of Point A as \( A = -d \), where \( d \) is a positive distance below sea level.

Point B is plotted above 0 at a distance exactly equal to the distance of Point A from 0. Since Point A is \( -d \), its distance from 0 is \( |A| = d \). Therefore, Point B must be positioned \( d \) units above 0, which gives it a positive value.

Thus, we can express the value of Point B as \( B = d \). In summary:

• Point A is below sea level and negative (e.g., \( -5 \) if \( d = 5 \)).
• Point B is directly above sea level and positive, at the same numerical distance from 0 (e.g., \( 5 \) if \( d = 5 \)).

Point B is the positive counterpart of Point A in terms of distance from 0 on the number line.