The line 3x + 2y = 24 meets the y-axis at A and the x-axis at B. The perpendicular bisector of AB meets the line through (0, -1) parallel to the x-axis at C. The area of triangle ABC is

Line 3x + 2y = 24 meets the axes at, B(8, 0) and A(0, 12). The midpoint of AB is D(4, 6).
The equation of perpendicular bisector of AB is 2x-3y+10=0 ………..(1)
Now, the line through (0, -1) and parallel to the x-axis is y = -1.
The coordinates of C where line (1) meets .y= -1 are (-13/2,-1).
Now, the area of triangle ABC,

$\begin{array}{rl}\mathrm{\Delta }& =\frac{1}{2}\left|\left|\begin{array}{ccc}0& 12& 1\\ 8& 0& 1\\ -13/2& -1& 1\end{array}\right|\right|\\ & =\frac{1}{2}\left|\left[0-12\left(8+\frac{13}{2}\right)+1(-8)\right]\right|=\frac{1}{2}\left|[-6(29)-8]\right|=91\end{array}$