SSC Sample Paper Mock Test-6 SSC CGL Tear-II Paper-1

In each of the following, find the value of k, for which the points are collinear \[(7,-\,\,2),\]\[(5,1),\]\[(3,k)\]

A) 4

B)                    5

C) 3

D) 2

Correct Answer: A

Solution :

Let \[A=({{x}_{1}},{{y}_{1}})=(7,-2),\]\[B=({{x}_{2}},{{y}_{2}})\]

\[=(5,1)\] and \[C=({{x}_{3}},{{y}_{3}})=(3,k)\]

Since, the points are collinear,

Area of \[\Delta ABC=0\]

\[\Rightarrow \]\[\frac{1}{2}[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})]=0\]

\[\Rightarrow \]\[7(1-k)+5\,\,(k+2)+3\,\,(-2-1)=0\]

(Multiply by 2)

\[\Rightarrow \] \[7-7k+5k+10-9=0\]

\[\Rightarrow \] \[-\,\,2k+8=0\]

\[\Rightarrow \] \[2k=8\]

\[\therefore \] \[k=4\]