A) 2
B) 4
C) 6
D) 9
Correct Answer: D
Solution :
[d] Given,\[{{x}_{1}}=1,\]\[{{x}_{2}}=5,\]\[{{x}_{3}}=k\] \[{{y}_{1}}=-1,\] \[{{y}_{2}}=2,\] \[{{y}_{3}}=5\] Since, A, B and C are collinear, \[\therefore \] \[\Delta =0\] \[\Rightarrow \]\[\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}=0\] \[\Rightarrow \] \[\{1\,(2-5)+5\,(5-(-1)+k\,(-1-2)\}=0\] \[\Rightarrow \] \[\{-3+30-3k\}=0\] \[\therefore \] \[k=9\] |
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