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) |
\[\Rightarrow \] \[7-7k+5k+10-9=0\] |
\[\Rightarrow \] \[-\,\,2k+8=0\] |
\[\Rightarrow \] \[2k=8\] |
\[\therefore \] \[k=4\] |
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