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The line 3x+2y= 4 meets the y axis at A and x axis at B. The perpendicular bisector meets the line through (0,-1) parallel to x axis at C . Fund the area of triangle ABC.

The line 3x+2y= 4 meets the y axis at A and x axis at B. The perpendicular bisector meets the line through (0,-1) parallel to x axis at C . Fund the area of triangle ABC.

Grade:11

1 Answers

Vikas TU
14149 Points
3 years ago
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

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