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The point P(alpha,alpha +1) will lie ins...

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

A

A. `alpha =- 1`

B

B. `alpha =- (1)/(2)`

C

C. `alpha = (1)/(2)`

D

D. `-(6)/(7) lt alpha lt (3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
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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