Question
The range of value of $$\alpha $$ such that $$\left( {0,\,\alpha } \right)$$ lies on or inside the triangle formed by the lines $$y + 3x + 2 = 0,\,3y - 2x - 5 = 0,\,4y + x - 14 = 0\,{\text{is :}}$$
A.
$${\text{5 < }}\alpha \leqslant 7$$
B.
$$\frac{1}{2} \leqslant \alpha \leqslant 1$$
C.
$$\frac{5}{3} \leqslant \alpha \leqslant \frac{7}{2}$$
D.
None of these
Answer :
$$\frac{5}{3} \leqslant \alpha \leqslant \frac{7}{2}$$
Solution :
Point $$\left( {0,\,\alpha } \right)$$ lies on the $$y$$-axis. In such questions, it is easier to see the location of point if lines are drawn on the axis.
From the diagram, it is clear that $$\frac{5}{3} \leqslant \alpha \leqslant \frac{7}{2}$$
Point $$\left( {0,\,\alpha } \right)$$ lies on the $$y$$-axis. In such questions, it is easier to see the location of point if lines are drawn on the axis.
From the diagram, it is clear that $$\frac{5}{3} \leqslant \alpha \leqslant \frac{7}{2}$$