1.

The point P(alpha,alpha +1) will lie inside the triangle whose vertices are A(0,3), B(-2,0) and C(6,1) if

Answer»

`alpha =- 1`
`alpha =- (1)/(2)`
`alpha = (1)/(2)`
`-(6)/(7) lt alpha lt (3)/(2)`

Solution :We have `A(0,3), B(-2,0)` and `C(6,1)`
Equation of AC is `X +3y - 9 =0`
Equation of BC is `x - 8y +2 = 0`

`P (alpha, alpha +1)` lies on the line `y = x +1`
whichcuts BC at `D(-(6)/(7),(1)/(7))` and AC at `E ((3)/(2),(5)/(2))`
`:. alpha` must lie between `-(6)/(7)`and `(3)/(2)`.


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