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`

Explanation

We have given the coordinates of `A ,B ,C`
as `(6,3),(-3,5),(4,-2)`

So, Area`\DeltaABC=(1/2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

`⇒`Areaof`\Delta ABC= (1/2)|6(7)-3(-5)+4(-2)|`

`=(1/2)|42+15-8|`

`=(1/2)|49|`

Area`\Delta ABC=(1/2)|49|` unit square

Area`\Delta PBC=(1/2)|x(7)-3(-2-y)+4(y-5)|`

...