Suppose a diver dives from a platform 4 feet above the water and stops at -8 feet to pick up some scallops. Which expression models this situation and tells how far below the platform the diver is?
A) $|4|+|8|$
B) $-4+|-8|$
C) $4-|-8|$
D) $4+|-8|$
Answer (2)
The expression that models how far below the platform the diver is, is 4 + ∣ − 8∣ . This means the diver is 12 feet below the platform. Therefore, the correct choice is D) 4 + ∣ − 8∣ .
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The diver starts 4 feet above the water.
The diver dives to -8 feet, which is a distance of ∣ − 8∣ from the water surface.
The total distance below the platform is the sum of the platform's height and the diver's depth: 4 + ∣ − 8∣ .
The expression that models this situation is 4 + ∣ − 8∣ .
Explanation
Initial Position The diver starts at a platform 4 feet above the water. This means the starting point is +4 feet relative to the water surface.
Diver's Depth The diver then dives to -8 feet, which is 8 feet below the water surface. We use the absolute value to represent the distance below the surface.
Total Distance Calculation To find the total distance the diver is below the platform, we need to add the initial height of the platform above the water (4 feet) to the depth the diver reached below the water surface (|-8| = 8 feet).
The Expression Therefore, the expression that models this situation is 4 + ∣ − 8∣ .
Examples
Understanding the concept of distance and absolute values is crucial in various real-life scenarios. For instance, consider a building with floors above and below ground level. If you start on the 4th floor and go down to the -8th floor (8 floors below ground), the total distance you traveled is represented by the same expression: 4 + ∣ − 8∣ = 12 floors. This concept is also applicable in finance when tracking gains and losses relative to an initial investment, or in geography when calculating elevation changes above and below sea level.
