Answer:
Given, \[A(2,1),B(3,-2)\] and \[C\left( \frac{7}{2},y \right)\] Now, Area \[(\Delta ABC)=\frac{1}{2}|{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})|\] \[5=\frac{1}{2}|2(-2-y)+3(y-1)+\frac{7}{2}(1+2)|\] \[\Rightarrow \] \[10=|-4-2y+3y-3+\frac{7}{2}+7|\] \[\Rightarrow \] \[10=\left| y+\frac{7}{2} \right|\] \[\Rightarrow \] \[10=y+\frac{7}{2}\] or \[-10=\left( y+\frac{7}{2} \right)\] \[\Rightarrow \] \[y=\frac{13}{2}\] or \[y=\frac{-27}{2}\]
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