A) \[182sq.\]units
B) \[91sq.\]units
C) \[48sq.\]units
D) None of these
Correct Answer: B
Solution :
The coordinates of A and B are \[(0,\,12)\]and \[(8,0)\] respectively. The equation of the perpendicular bisector of AB is \[y-6=\frac{2}{3}(x-4)\] or \[2x-3y+10=0\] .....(i) Equation of a line passing through (0, ?1) and parallel to x-axis is \[y=-1\]. This meets (i) at C, Therefore the coordinates of C are\[\left( -\frac{13}{2},-1 \right)\]. Hence the area of the triangle \[ABC\]is \[\Delta =\frac{1}{2}\left| \begin{matrix} 0 & 12 & 1 \\ 8 & 0 & 1 \\ -\frac{13}{2} & -1 & 1 \\ \end{matrix}\, \right|=91\] sq. units.You need to login to perform this action.
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