MathematicsThe value of p, for which the points A(3,1),B(5,p)and C(7,-5)are collinear, is

The value of p, for which the points A(3,1),B(5,p)and C(7,-5)are collinear, is


  1. A
    -2
  2. B
    2
  3. C
    -1
  4. D
    1  

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    Solution:

    Given  A(3,1),B(5,p)and C(7,-5)are collinear.
    We know that the area of the triangle whose vertices are (x1,y1),(x2,y2),and (x3,y3) is =12|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|.
    Now, if points A(x1,y1),B(x2,y2),C(x3,y3) are collinear then,
     Area(△ABC)=12[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]=0 ⇒ 12[3[5+p)+5(-5-1)+7(1-p)]=0 ⇒ 15+3p-30+7-7p=0 ⇒  4p=-15+7 ⇒ 4p=-8 ⇒  p=-2 So the correct option is 1.
     
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