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Question

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


Solution

Given line 3x+2y=24
Now, the points 
A=(0,12),B=(8,0)
Midpoint of line segment AB
=(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
=12x1x2x3x1y1y2y3y1=12∣ ∣081320120112∣ ∣=12|96878|=91 sq. units

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