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Four points A(6,3),B(-3,5),C(4,-2) and D...

Four points `A(6,3),B(-3,5),C(4,-2)` and `D(x ,2x)` are given in such a way that `((A r e aofD B C))/((A r e aofA B C))=1/2dot`

Text Solution

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The correct Answer is:
`(11)/(6)`
`("Area of"DeltaDBC)/("Area of"DeltaABC)=(1)/(2)`
or `((1)/(2)[x(5+2)-3(-2-2x)+4(2x-5)])/((1)/(2)[6(5+2)-3(-2-3)+4(3-5)])=(1)/(2)`
or `(7x+6+6x+8x-20)/(42+15-8)=(1)/(2)`
or `(3x-2)/(7)=(1)/(2)` or `x=(11)/(6)`
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