MathematicsFor what value of x   are the points A(−3,12),B(7,6)  and C(x,9)   collinear?

For what value of x   are the points A(−3,12),B(7,6)  and C(x,9)   collinear?


  1. A
    2
  2. B
    4
  3. C
    6
  4. D
    8 

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    Solution:

    We are given the points as  and .
    Given A(−3,12),(B7,6)   and C(x,9)   are collinear.
    Here,
    x 1 =−3, x 2 =7, x 3 =x, y 1 =12, y 2 =6, y 3 =9.  
    Apply the condition that, 3 points are collinear if the area between the points that is the area of triangle is zero in the given points.
    Area of a triangle with vertices and   is given by,
    ⇒0×2=−12+6x ⇒6x=12 ⇒x=2  
    Value of x for which the given points become collinear is 2.
    Hence, correct option is 1.
     
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