(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether the points lie on a straight line.

a) A(2,4,2), B(3,7,-2), C(1,3,3)

b) D(0,-5,5), E(1,-2,4), F(3,4,2)

2. Relevant equations

3. The attempt at a solution

I tried graphing to see the points A B and C to see if they looked like they were in a straight line and it looked like they were but the answer says they are not in a straight line. I looked on Cramster and they said, "For the points to be in a straight line, the distance between the two sets of points closest to each other must equal the distance between the two points farthest from each other." I am not following this logic. Our solution manual for our class says, "In order for the points to lie on a straight line, the sum of the two shortest distances must be equal to the longest distance." This made a little more sense so I tried to test this by doing it in 2D. I graphed the line y=x and chose 3 points: (0,0), (1,1), and (2,2). It turned out that their method worked for 2D and according to the graph I drew, it looks obvious that the the distance from (0,0) to (1,1) plus the distance from (1,1) to (2,2) equals the distance from (0,0) to (2,2) but I can't seem to visualize/see it graphically in 3D. Any tips? Thanks

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Determine whether the points lie on a straight line

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