• # question_answer The line $3x+2y=24$meets $y$-axis at A and x-axis at B. The perpendicular bisector of $AB$meets the line through $(0,-1)$ parallel to x-axis at C. The area of the triangle $ABC$ is  A)            $182sq.$units                          B)            $91sq.$units C)            $48sq.$units                            D)            None of these

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.