Quantitative Aptitude Ques 1274

Question: Find the value of k for which the points $ A(-1,3), $ $ B(2,k) $ and $ C(5,-1) $ are collinear

Options:

A) 1

B) 3

C) 2

D) 4

Show Answer

Answer:

Correct Answer: A

Solution:

  • Here, $ x _1=-1, $ $ x _2=2, $ $ x _3=5, $ $ y _1=3, $ $ y _2=k $ and $ y _3=-1 $ Since, points are collinear, Then, area $ (\Delta )=0 $

$ \Rightarrow $ $ x _1(y _2-y _3)+x _2(y _3-y _1)+x _3(y _1-y _2)=0 $

$ \Rightarrow $ $ -1(k+1)+2(-1-3)+5(3-k)=0 $

$ \Rightarrow $ $ -k-1-8+15-5k=0 $

$ \Rightarrow $ $ 6k=6 $
$ \Rightarrow $ $ k=1 $

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