To determine whether a third alien could have been rescued on the same trip while picking up the other two stranded aliens, we need to consider whether the pickup of the two aliens allows for a third alien to be on the same route.
In a single trip, we need to assess the distances involved based on the given coordinates of the aliens.
Let's assume you can only pick up two aliens at a time. The aliens are located at coordinates (2, –5), (1, 2), and (-2, –3). According to the question, we need to analyze all possible combinations of picking two of them and see if the third can be included in the trip.
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First combination: Picking up (2, –5) and (1, 2)
- The origin point is (0, 0). The distance to (2, –5) is approximately 5.385, and to (1, 2) is approximately 2.236. The distance between these two points is approximately 3.605.
- The overall trip could mean going to (2, –5) to (1, 2) before returning to the origin, or vice versa.
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Second combination: Picking up (2, –5) and (-2, –3)
- The distance to (-2, –3) is approximately 3.605, while we previously calculated the distance to (2, -5). The distance between these two points also needs to be taken into account.
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Third combination: Picking up (1, 2) and (-2, –3)
- Similarly, we'd consider the distances from the origin to each point and assess the route.
In all cases, you could potentially circle back to rescue any remaining alien provided they fall within the trip route between other two or back to origin.
So, the answer to the question: For a third alien to have been rescued on the same trip, he could have been located at the origin (0, 0). By picking two aliens that are nearer to the origin and looping back, it’s feasible for the third alien to be picked up if they were at the origin.
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