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Home  >>  CBSE XI  >>  Math  >>  Straight Lines
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State whether the following statement is true or false and justify : The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear

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  • Area of a triangle is given by $ \Delta = \large\frac{1}{2} | x_1 (y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$
  • If the three points are collinear then $ \Delta = 0 $ (i.e) $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$
Step 1 :
Let A(-2, 1) be $(x_1, y_1)$
$ \quad \: $ B(0,5 ) be $(x_2, y_2)$
$ \quad \: $ C(-1,2 ) be $(x_3, y_3)$
Substituting the above value in $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) $ we get,
$-2(5-3)+0(2-1)+(-1)(1-5)$
$ = -4+0+4=0$
Hence the points are collinear.
Hence it is a true statement.
answered Jul 8, 2014 by thanvigandhi_1
 

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