figure below, a highway rest area (at D) and radar stations (at A and B) lie on a level east-west line; A is 9,000 feet due west of D. An airplane (at C) is shown directly above the rest area, flying due west at a constant speed of 300 feet per second and at a constant altitude of12,000 feet. The airplane is located at a straight-line distance of 15,000 feet from the radar station at A and 13,000 feet from the radar station at B.Let A, C, and D lie in the standard (x,y) coordinate plane such that A is at (0,0) and D is at (9,000, 0). Which of the following equations represents the line along which the airplane is flying ?
Question
figure below, a highway rest area (at D) and radar stations (at A and B) lie on a level east-west line; A is 9,000 feet due west of D. An airplane (at C) is shown directly above the rest area, flying due west at a constant speed of 300 feet per second and at a constant altitude of12,000 feet. The airplane is located at a straight-line distance of 15,000 feet from the radar station at A and 13,000 feet from the radar station at B.Let A, C, and D lie in the standard (x,y) coordinate plane such that A is at (0,0) and D is at (9,000, 0). Which of the following equations represents the line along which the airplane is flying ?
Solution
The airplane is flying due west at a constant altitude. In the context of the coordinate plane, this means that the y-coordinate (representing altitude) is constant, while the x-coordinate (representing east-west position) is decreasing as the plane moves west.
Since the plane is directly above D at the start, it starts at the point (9000, 12000). As it moves west, the x-coordinate decreases, but the y-coordinate stays the same.
Therefore, the line along which the airplane is flying is represented by the equation y = 12000.
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