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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 (0,1) parallel to x-axis at C. Find the area of the ABC.

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. units
A(0,12),B(8,0)

D the mid point of AB is (4,6)

Equation of the perpendicular bisector is

2x3y=2×43×6=10

which meets the line y=1 at C(132,1)

Area of triangle ABC

=12AB×CD

=1264+144+(4+132)2+(6+1)2

=12×413×7(32)2+1

=13×7=91

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