Question

The point which does not lie in the half plane
2x + 3y − 12 ≤ 0 is
(a) (1,2) (b) (2,1) (c) (2,3) (d)(−3, 2)

Answer 1

Answer:

The option C is correct.

Explanation:

The points which does not lie in half plane are (2,3).

Reason:

When we put x=2 and y=3 in equation then

2(2)+3(3)-12<=0

4+9-12<=0

13-12<=0

1<=0

which is not true so these points does not lie in the half plane.

Answer 2

The point which does not lie in the half plane 2x + 3y − 12 ≤ 0 is (2,3) and option (c) is correct.

Explanation:

Given:

The half plane equation 2x + 3y − 12 ≤ 0.

The points (a) (1,2)   (b) (2,1)     (c) (2,3)    (d)(−3, 2).

To Find:

The point which does not lie in the half plane 2x + 3y − 12 ≤ 0  from the given points (a) (1,2)   (b) (2,1)   (c) (2,3)   (d)(−3, 2).

Solution:

As given, the half plane equation 2x + 3y − 12 ≤ 0.

Then,  the point on half plane 2x + 3y − 12 > 0 does not lie in the given half plane.

⇒ 2x + 3y > 12.

The points which satisfies inequality 2x + 3y > 12 does not lie on the given half plane.

(a) For Point (1,2)

     Putting $x=1 \ and\ y=2$ in the  equation

     $2x + 3y > 12$

      $2\times 1+3\times 2 > 12\\2+6 > 12\\8 > 12$

     Which is not true.

(b) For Point (2,1)

     Putting $x=2 \ and\ y=1$ in the  equation

     $2x + 3y > 12$

     $2\times 2+3\times 1 > 12\\4+3 > 12\\7 > 12$

     Which is not true.

(c) For Point (2,3)

     Putting $x=2 \ and\ y=3$ in the  equation

     $2x + 3y > 12$

     $2\times 2+3\times 3 > 12\\4+9 > 12\\13 > 12$

     Which is  true.

(d) For Point (-3,2)

     Putting $x=-3 \ and\ y=2$ in the  equation

     $2x + 3y > 12$

     $2\times (-3)+3\times 2 > 12\\-6+6 > 12\\0 > 12$

     Which is not true

Thus,the point which does not lie in the half plane 2x + 3y − 12 ≤ 0 is (2,3) and option (c) is correct.

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