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:

  1. 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.



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