First slide

Equation of line in Straight lines

Question

The condition to be imposed on $β$ so that (0, $β$ ) lies on or inside the triangle having sides y + 3x + 2 = 0, 3y – 2x – 5 = 0 and 4y + x – 14 = 0 is

Moderate

A

$0 < β < \frac{5}{3}$
B

$0 < β < \frac{7}{2}$
C

$\frac{5}{3} \leq β \leq \frac{7}{2}$
D

none of these

Solution

Clearly point (0, $β$ ) lies on y-axis.
Drawing the graph of the three straight lines, we see that
$Q = (0, \frac{7}{2}) a n d P \equiv (0, \frac{5}{3})$
Therefore, the point (0, $β$ ) lies on or inside $∆$ ABC, when
$\frac{5}{3} \leq β \leq \frac{7}{2}$

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