The point which does not lie in the half plane 2x + 3y – 12 0 is,

Given: Half plane 2x + 3y – 12 0

To Find: Which of the given points doesn’t satisfy the equation of the plane.

Here we have to check which point doesn’t satisfy the given equation.

For the point (1, 2), putting x = 1 and y = 2 in the given equation,

2 1 + 3 2 – 12

= 2 + 6 – 12

= -4 0

So, the given equation is true for this point.

For the point (2, 1), putting x = 2 and y = 1 in the given equation,

2 2 + 3 1 – 12

= 4 + 3 – 12

= -5 0

So, the given equation is true for this point also.

For the point (2, 3), putting x = 2 and y = 3 in the given equation,

2 2 + 3 3 – 12

= 4 + 9 – 12

= 1 0

So, the given equation is false for this point. That means this point (2, 3) doesn’t lie on the given half plane.

For the point (-3, 2), putting x = -3 and y = 2 in the given equation,

2 (-3) + 3 2 – 12

= -6 + 6 – 12

= -12 0

So, the given equation is true for this point also.

Therefore, we can conclude that the point (2, 3) is the only point which doesn’t lie on the given half plane.