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Billy was standing on a diving board that was 4 feet above the water. He dove into the pool which was 8 feet deep and touched the bottom. Which statement accurately describes this situation?A. If 0 represents the height of the diving board, then +4 represents the water level and –8 represents the bottom of the pool.B. If +4 represents the height of the diving board, then 0 represents the water level and –8 represents the bottom of the pool.C. If 0 represents the height of the diving board, then 4 represents the water level and 8 represents the bottom of the pool.D. If +8 represents the height of the diving board, then 0 represents the water level and –4 represents the bottom of the pool.

1 answer

To evaluate the statements correctly, we can use a number line where:

  • The water level is established as the reference point (0).
  • The diving board is above the water level, so it will be represented as a positive value.
  • The bottom of the pool is below the water level and will be represented as a negative value.

Given:

  • The height of the diving board is +4 feet above the water.
  • The depth of the pool is 8 feet, which means the bottom of the pool is 8 feet below the water level, or -8 feet.

Now let's analyze each statement:

A. If 0 represents the height of the diving board, then +4 represents the water level and –8 represents the bottom of the pool.

  • Incorrect. This misrepresents the heights.

B. If +4 represents the height of the diving board, then 0 represents the water level and –8 represents the bottom of the pool.

  • Correct. This accurately defines the diving board, water level, and bottom of the pool.

C. If 0 represents the height of the diving board, then 4 represents the water level and 8 represents the bottom of the pool.

  • Incorrect. This misrepresents the heights again.

D. If +8 represents the height of the diving board, then 0 represents the water level and –4 represents the bottom of the pool.

  • Incorrect. This incorrectly defines the positions relative to the water level.

The correct statement is B: If +4 represents the height of the diving board, then 0 represents the water level and –8 represents the bottom of the pool.