10.1.3 Formulas in Three Dimensions (continued)
The length and midpoint of a line segment defined by two endpoints in three dimensions is determined in this example. The coordinates of the endpoints are given. To determine the distance between the two endpoints, substitute the coordinates into the Distance Formula in Three Dimensions. The solution for the distance is the square root of 41 units. To determine the midpoint of the line segment with the given endpoints, substitute the coordinates into the Midpoint Formula in Three Dimensions. The solution for the midpoint of the line segment is M (3/2, 4, 7). The straightline distance between two points is determined in this application example. The coordinates of the points are given in three- dimensional space. Begin by determining the coordinates of the two people relative to the origin, which is the water cooler. A diagram is a useful way of visualizing the movements on the three axes and organizing the information. The x , y , z coordinates of the first person are ( − 20, 10, 12). The coordinates of the second person are (15, − 9, − 24). To find the distance between the people, substitute the coordinates into the Distance Formula in Three Dimensions. Using a calculator, the distance is found to be approximately 53.68 feet.
Example 5 Office Application
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