The two people are distanced by 39.1 feet after going through the allotted areas.
How is the distance between two three-dimensional points calculated?
The distance formula can be used to compute the distance (d) between two points in the three-dimensional coordinate system (x₁, y₁, z₁) and (x₂, y₂, z₂).
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²).
How do we solve the given question?
We are informed that two people meet in the purple room on the fourth floor of a building. On departure, one person travels West 16 feet, South 9 feet, and Down 9 feet, while the other person travels 16 feet north, 8 feet east, and 9 feet up.
We are asked to calculate the distance between two people.
To determine the distance, we take the given conditions on a three-dimensional coordinate plane, with the purple room on the fourth floor as the origin.
The east-west line represents the x-axis, east positive and west negative.
The north-south line represents the y-axis, north positive and south negative.
The up-down line represents the z-axis, up positive and down negative.
∴ The two people are now located at (-16, -9, -9) and (8, 16, 9)
We can find the distance between these points using the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
or, d = √((8 - (-16))² + (16 - (-9))² + (9 - (-9))²)
or, d = √((8 + 16)² + (16 + 9)² + (9 + 9)²)
or, d = √(24² + 25² + 18²)
or, d = √(576 + 625 + 324) = √1525 = 39.051248
or, d = 39.1 (rounding to the nearest tenth of a foot).
∴ The two people are distanced by 39.1 feet after going through the allotted areas.
Learn more about the three-dimensional coordinate plane at
brainly.com/question/24289673
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