Question

Finding the Equation of a Line That Connects Four Points

There are only two more stranded aliens. See if you can pick them up in a single trip. Then answer the question.

For a third alien to have been rescued on the same trip, where could he have been located?

the origin
(2, –5)
(1, 2)
(-2, –3)

Answer 1

No — none of those points could be the third alien. No three of the four points are collinear.

Checking slopes between every pair:
- slope( (0,0),(2,-5) ) = -5/2
- slope( (0,0),(1,2) ) = 2
- slope( (0,0),(-2,-3) ) = 3/2
- slope( (2,-5),(1,2) ) = -7
- slope( (2,-5),(-2,-3) ) = -1/2
- slope( (1,2),(-2,-3) ) = 5/3

No two of these slopes are equal, so no single line goes through three of the points. Thus none of the listed locations could be the third alien rescued on that same straight trip.