If the point $(a, 2)$ lies between the lines $x - y - 1 = 0$ and $2 (x - y) - 5 = 0$ then the set of values of $a$ is

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Solution

$L_{1} : x - y - 1 = 0$
$L_{2} : 2 (x - y) - 5 = 0$
Since, $L_{1} | | L_{2}$
point $(a, 2)$ lies in side the region
when $a - 2 - 1 > 0$ and $a - 2 - \frac{5}{2} < 0$
$\Rightarrow a > 3$ and $a < \frac{9}{2}$
$∴ a \in (3, \frac{9}{2})$

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(i) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (2, 3).

(ii) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (4, -6).

(iii) the point (8, 7) lies on the line y - 7 = 0

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(v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

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