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  • State whether the statements are true or false. The points A minus 2, 1, B 0, 5, C minus 1, 2 are collinear.

State whether the statements are true or false.

The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear.

Answers (1)

Given points are A(-2,1), B (0,5) and C(-1,2)   

 There are two ways to find that given points are collinear or not .

   The first is if 3 points are collinear, then slope of any two pairs of points will be equal.  

 Second way is that if the value of area of triangle formed by the 3 points is zero, then the points

 are collinear.  

 Slope of AB  m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{5-1}{0-\left ( -2 \right )}=2

  Slope of BC  m==\frac{2-5}{-1-0}=\frac{3}{-1}=3

  Slope of CA ism==\frac{1-2}{-2-\left ( -1 \right )}=\left (-\frac{1}{-2+1} \right )=1

  Since, the slopes are different.

 So, the given points are not collinear

  Hence, the given statement is False 

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