Line 3x + 2y =24 meets x-axis at A and y- axis at B and perpending bisector of AB meets the line passing through (0,1) and parallel to x-axis at C. Area of ` Delta ABC` is

Options

A. 182 sq units
B. 91 sq units
C. 48 sq units
D. none of these

Answer

C

Explanation

`3x+ 2y =24`
` (x)/(8)+(y)/(12)=1`
` A(8,0),b(0,12)`
Now perpendicular bisector of AB : 2X - 3Y = `lamda` passes through (4,6)
`implies lamda =-10` ,
` implies` equation
`implies 2x - 3y + 10 =0`
` (##CP_JM_MT_08_E01_076_S01.png" width="80%">
`Delta=(1)/(2)|{:(8,0,1),(0,12,1),((-13)/(2),-1,1):}|=91`