A) \[4\]
B) \[6\]
C) \[\frac{-\,\,3}{2}\]
D) \[\frac{11}{4}\]
Correct Answer: B
Solution :
Here \[{{x}_{1}}=2,\]\[{{x}_{2}}=5,\]\[{{x}_{3}}=6,\]\[{{y}_{1}}=3,\]\[{{y}_{2}}=k\]and \[{{y}_{3}}=7.\] \[\Delta =0\]\[\Leftrightarrow \]\[\frac{1}{2}\cdot \{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}\]\[=0\] \[\Leftrightarrow \]\[2\,\,(k-7)+5\,\,(7-3)+6\,\,(3-k)=0\]\[\Leftrightarrow \]\[4k-24\]\[\Leftrightarrow \]\[k=6\]
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