A) 6
B) \[-\,\,3\]
C) 9
D) 4
Correct Answer: C
Solution :
Here,\[{{x}_{1}}=1,\]\[{{x}_{2}}=5,\]\[{{x}_{3}}=k,\]\[{{y}_{1}}=-1,\]\[{{y}_{2}}=2,\]\[{{y}_{3}}=5\] \[\Delta =0\]\[\Leftrightarrow \]\[\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}\]\[=0\] \[\Leftrightarrow \] \[1\cdot (2-5)+5\,\,(5+1)+k\,\,(-1-2)=0\] \[\Leftrightarrow \] \[-3+30-3k=0\]\[\Leftrightarrow \]\[3k=27\]\[\Leftrightarrow \]\[k=9\]
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