Are the points (1, 1), (5, 5), and (7, -4) collinear? Explain.

The points (1,1), (5,5), and (7,-4) are not collinear because they do not lie on the same line.
To check for collinearity, we can calculate the slope between each pair of points and see if they are equal. The slope between (1,1) and (5,5) is (5-1)/(5-1) = 1, and the slope between (1,1) and (7,-4) is (-4-1)/(7-1) = -0.83. Since the slopes are not equal, the points are not collinear.
The points are also not coplanar because they do not lie in the same plane. In three-dimensional space, three points are coplanar if the volume of the parallelepiped formed by them is zero. Since the volume is non-zero for the given points, they are not coplanar.

Answered by Darla1012 | 2024-06-24

The points (1, 1), (5, 5), and (7, -4) are not collinear because the slopes between the points are not equal. The slope between (1, 1) and (5, 5) is 1, while the slope between (1, 1) and (7, -4) is − 6 5 ​ . Since the slopes differ, the points do not lie on the same straight line.
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Answered by Darla1012 | 2025-03-01