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Question

The line 3x+2y=24 meets the y-axis at A & the x-axis at B. The perpendicular bisector of AB meets the line through (0,âˆ’1) parallel to x-axis at C. Find the area of the â–³ABC.

A
91 sq. units
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B
5 sq.units
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C
182 sq.units
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D
10 sq.units
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Solution

The correct option is A 91 sq. unitsA(0,12),B(8,0) D the mid point of AB is (4,6)Equation of the perpendicular bisector is2x−3y=2×4−3×6=−10which meets the line y=−1 at C(−132,−1)Area of triangle ABC =12AB×CD=12√64+144+√(4+132)2+(6+1)2=12×4√13×7√(32)2+1=13×7=91

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