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,Δ=120121801−13/2−11 =120−128+132+1(−8)=12[−6(29)−8]=91