Question

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. 91 sq. Units
• C. 48 sq. Units
• D. 501 sq units

Answer 1

The correct option is B 91 sq. Units

The coordinates of A and B are (0, 12) and (8, 0) respectively. The equation of the perpendicular bisector of AB is $y-6=\frac{2}{3}(x-4)or2x-3y+10=0$ .....(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 $(-\frac{13}{2},-1)$.
Hence the area of the triangle ABC is
$\Delta =\frac{1}{2}\left|\begin{array}{ccc}0& 12& 1\\ 8& 0& 1\\ -\frac{13}{2}& -1& 1\end{array}\right|=91sq.units$