1.

Point A lies on the line `y=2x` and the sum of its abscissa and ordinate is 12. Point `B` lies on the x-axis and the line `AB` is perpendicular to the line `y=2x`. Let `O` be the origin. The area of the Delta AOB isA. 20B. 40C. 60D. 80

Answer» Correct Answer - D
Let `A(x_(1),y_(1))`
`x_(1)+y_(1)=12`
`y_(1)=12-x_(1)`
A lies on `y=2x`
`y_(1)=2x_(1)`
`12-x_(1)=2x_(1)`
`x_(1)=4`
Hence, `A=(4,8)` equation of AB is
`x+2y+lamda=0`
Eq. (i) passes through (4,8)
`becauselamda=-20`
`x+2y=20impliesB` is `(20,0)`
Area of `DeltaAOB=(20.8)/(2)=80` sq unit


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