Straight Line and Pair of Straight Lines 1 Question 43
43. All points lying inside the triangle formed by the points $(1,3),(5,0)$ and $(-1,2)$ satisfy
$(1986,2 M)$
(a) $3 x+2 y \geq 0$
(b) $2 x+y-13 \geq 0$
(c) $2 x-3 y-12 \leq 0$
(d) $-2 x+y \geq 0$
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Solution:
- Since, $3 x+2 y \geq 0$
where $(1,3)(5,0)$ and $(-1,2)$ satisfy Eq. (i).
$\therefore$ Option (a) is true.
Again, $\quad 2 x+y-13 \geq 0$
is not satisfied by $(1,3)$,
$\therefore$ Option (b) is false.
$$ 2 x-3 y-12 \leq 0 $$
is satisfied for all points,
$\therefore$ Option (c) is true.
and
$$ -2 x+y \geq 0 $$
is not satisfied by $(5,0)$,
$\therefore$ Option (d) is false.
Thus, (a) and (c) are correct answers.
