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Question

The line 3x2y=24 meets xaxis at A and y axis at B. The perpendicular bisector of AB meets the line through (0,1) and parallel to xaxis at C. Then C is

A
(72,1)
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B
(152,1)
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C
(112,1)
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D
(132,1)
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Solution

The correct option is A (72,1)
Slope of the line joining of AB is 32 and it's mid-point is M(4,6).
The perpendicular bisector of this line will have the slope 23 and pass through M(4,6)................(using m1.m2= -1 product of slopes of two perpendicular lines)
The equation of the perpendicular bisector of AB is 2x+3y+10=0(1).
The equation of the other line given in the problem is y=1(2).
Lines (1) and (2) intersect at (72,1).

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