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Question

Let the line 3x+2y=24 meet yaxis at A and xaxis at B. If the perpendicular bisector of AB meets the line y=1 at C, then the area of the ABC (in sq. units) is

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Solution

Given line 3x+2y=24
So, A(0,12),B(8,0)
Mid-point of line segment AB is (4,6)
The equation of the perpendicular bisector of AB is
y6=80012(x4)3y18=2x82x3y+10=0
This line meets the y=1 at C(132,1)

Thus, the area of the ABC is
12x1x2x3x1y1y2y3y1

=12∣ ∣081320120112∣ ∣=12|96878|=91 sq. units

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