Determine whether the three points are colinear (0,-4),(-3,-18),(2,6) are the three points colinear?

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  they are not collinear

Step-by-step explanation:

A graph shows that a line through points A and C misses point B, so the points are not collinear.

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If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.

  m = (y2 -y1)/(x2 -x1)

  m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB

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  m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB

The points are not collinear.

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Additional comment

With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.

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