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Question 319677: Use the distance formula to determine whether the points lie on the same line: (0,-4), (2,0), (3,2)
(The only way I thought of doing this question is forming a right triangle with two of the points as the hypotenuse and plot the other point, but that really doesn't have so much to do with the distance formula. I have no idea how an equation made to house two points (which is what a line is, basically) can determine the presence of a third point given something as exclusive as distance, which would have to change anyway. But maybe that's just my way of thinking about it.)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Use the distance formula to determine whether the points lie on the same line: (0,-4), (2,0), (3,2)
(The only way I thought of doing this question is forming a right triangle with two of the points as the hypotenuse and plot the other point, but that really doesn't have so much to do with the distance formula. I have no idea how an equation made to house two points (which is what a line is, basically) can determine the presence of a third point given something as exclusive as distance, which would have to change anyway. But maybe that's just my way of thinking about it.)
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I don't understand your approach, but I don't see how the distance formula would help, either.
Label the points A, B & C for convenience.
A(0,-4), B(2,0), C(3,2)
Find the slope of AB and the slope of BC.
If they're equal, and share the middle point, B, then they're colinear.
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