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Four points A(6,\ 3),\ \ B(-3,\ 5),\ ...

Four points `A(6,\ 3),\ \ B(-3,\ 5),\ \ C(4,\ -2)` and `D(x ,\ 3x)` are given in such a way that `( D B C)/( A B C)=1/2` , find `x` .

Text Solution

Verified by Experts

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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