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

Options

A. A. `alpha =- 1`
B. B. `alpha =- (1)/(2)`
C. C. `alpha = (1)/(2)`
D. D. `-(6)/(7) lt alpha lt (3)/(2)`

Answer

B, C, D

Explanation

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)`.