Which point belongs to the region represented by $x + y \leq 0$ ?

(4, 5)

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(- 7, 9)

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(7, - 9)

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(8, - 12)

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Solution

The correct options are
C $(7, - 9)$
D $(8, - 12)$
By option verification,
i.e., substituting the options in given equation and verifying

Given $x + y \leq 0$

substituting option A i.e. $(x, y) = (4, 5)$

$4 + 5 \leq 0 ⟹ 9 \leq 0 ⟹$ False

substituting option B i.e. $(x, y) = (- 7, 9)$

$- 7 + 9 \leq 0 ⟹ 2 \leq 0 ⟹$ False

substituting option C i.e. $(x, y) = (7, - 9)$

$7 + (- 9) \leq 0 ⟹ - 2 \leq 0 ⟹$ True

substituting option D i.e. $(x, y) = (8, - 12)$

$8 + (- 12) \leq 0 ⟹ - 4 \leq 0 ⟹$ True

Therefore, $(7, - 9)$ and $(8, - 12)$ belongs to the region $x + y \leq 0$

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