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Let's denote the elevation of Point A, which is below sea level, as

, where
is a positive distance below sea level. Therefore, Point A can be represented as:

Given that Point B is plotted above 0 at a distance exactly equal to the distance of Point A from 0, we can determine the distance of Point A from 0. The distance from 0 to Point A is:

As Point B is positioned
units above 0, we find the elevation of Point B to be:

Thus, we can summarize the relationships between Points A and B:

Point A is below sea level and negative, for example,
if
would be
.
Point B is directly above sea level and positive, at the same numerical distance from 0, for example,
would be
.
Point B is the positive counterpart of Point A in terms of distance from 0 on the number line.
In conclusion, the values can be summarized as follows:

1 answer

Let's summarize the information given about Points A and B in a structured way:

  1. Elevation of Point A:

    • Point A is represented as \( A = -d \), where \( d \) is a positive distance below sea level. This means Point A is located at a negative elevation.

  2. Distance from 0 to Point A:

    • The distance from 0 to Point A is \( |A| = |-d| = d \). This indicates that the absolute value (or distance) from sea level (0) to Point A is \( d \).

  3. Elevation of Point B:

    • Point B is positioned \( d \) units above 0, hence its elevation can be expressed as \( B = d \). Point B is located at a positive elevation that is the same numerical value as the distance from Point A below sea level, but on the positive side.

  4. Relationship Summary:

    • Point A (negative elevation) is a distance \( d \) below sea level, for example, if \( d = 200 \) then \( A = -200 \).
    • Point B (positive elevation) is at an elevation \( d \) above sea level, for example, if \( d = 200 \) then \( B = 200 \).
    • Point B is thus the positive counterpart of Point A, maintaining the same absolute distance from 0 on the number line.

To conclude, if \( d \) is a positive distance:

  • Point A: \( A = -d \) (below sea level)
  • Point B: \( B = d \) (above sea level)

These values demonstrate a direct relationship where:

  • The elevation of Point A is always the negative of the elevation of Point B in terms of absolute value.