Question

Region represented by the inequalities x ≥ 0, y ≤ 0 is ______.

Options

• first quadrant

• second quadrant

• third quadrant

• fourth quadrant

Answer 1

Region represented by the inequalities x ≥ 0, y ≤ 0 is fourth quadrant.

Explanation:

Solution set of the given inequalities is

{(x, y) : x ≥ 0} ∩ {(x, y) : y ≤ 0} = {(x, y) : x ≥ 0, y ≤ 0}

i.e., the set of all those points whose abscissa are non-negative and ordinates are non-positive

All these points lie in the fourth quadrant (including points on +ve  X-axis, +ve Y-axis and the origin).