We have:3x+2y=24
For A put x=0
⇒2y=24
⇒y=12
Co−ordinates of A=(0,12)
For B put y=0
⇒3x=24
⇒x=8
⇒Co−ordinates of B=(8,0)
Mid purpose of Ab=(8+02,0+122)=(4,6)
Presently we will get condition of opposite bisector.
Condition of line opposite to 3x+2y=242x−3y=λ
It will go through mid purpose of AB i.e. (4,6)8−18=λ=−10⇒2x−3y=−10
Condition of line parallel to X−axis is:y=constantIt goes through (0,−1)
⇒−1=constant
⇒y=−1
To get co−ordinates of C, place y=−1 in 2x−3y=−10⇒2x+3=−10⇒x=−132
Henceforth we have C(−132,−1) and A(0,12) and B(8,0)
Region of ∆ABC=91unit2
