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
Options:
A) $ 182\text{ sq. }$ units
B) $ 91 sq. $ units
C) $ 48\text{sq.} $ units
D)None of these
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Answer:
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 $ ( -\frac{13}{2},-1 ) $ . Hence the area of the triangle $ ABC $ is $ \Delta =\frac{1}{2} \begin{vmatrix} 0 & 12 & 1 \\ 8 & 0 & 1 \\ -\frac{13}{2} & -1 & 1 \\ \end{vmatrix} |=91 $ sq. units.
BETA
