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The coordinates of A ,B ,C are (6,3),(-3...

The coordinates of `A ,B ,C` are `(6,3),(-3,5),(4,-2)` , respectively, and `P` is any point `(x ,y)` . Show that the ratio of the area of ` P B C` to that of ` A B C` is `(|x+y-2|)/7dot`

Text Solution

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`("Area of " DeltaPBC)/("Area of" DeltaABC)=((1)/(2)|x(5+2)+(-3)(-2-y)+4(y-5)|)/((1)/(2)|6(5+2)+(-3)(-2-3)+4(3-5)|)`
`=(|7x+7y-14|)/(|42+15-8|)=(7|x+y-2|)/(49)=|(x+y-2)/(7)|`
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