Question

 4. x≤0,y≤0 represents: *

1st Quadrant

2nd Quadrant

3rd Quadrant

4th Quadrant​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

x≤0,y≤0 represents: 

• 1st Quadrant

• 2nd Quadrant

• 3rd Quadrant

• 4th Quadrantt

EVALUATION

In the

1st quadrant : x is positive and y is positive

2nd quadrant : x is negative and y is positive

3rd quadrant : x is negative and y is negative

4th quadrant : x is positive and y is negative

Hence x≤0,y≤0 represents:  3rd Quadrant

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Answer 2

Given :- x ≤ 0 , y ≤ 0 represents :

A) 1st Quadrant

B) 2nd Quadrant

C) 3rd Quadrant

D) 4th Quadrant

Solution :-

we know that,

→ In 1st Quadrant :-

• x = + ve , y = + ve (Both positive)

→ In 2nd Quadrant :-

• x = - ve , y = + ve

→ In 3rd Quadrant :-

• x = - ve , y = - ve (Both negative)

→ In 4th Quadrant :-

• x = + ve , y = - ve

given that,

→ x ≤ 0 => x is always less than or equal to zero .

→ y ≤ 0 => y is always less than or equal to zero .

then, we can say that, both are less than or equal to 0 or both are negative.

therefore,

→ x ≤ 0 , y ≤ 0 = Both negative = Lies in 3rd quadrant .

Hence, we can conclude that the region represented by the inequalities x ≤ 0, y ≤ 0 lies in option (C) 3rd quadrant .

[ Note :- x ≥ 0, y ≥ 0 = Both positive = Lies in first quadrant . ]

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