In the diagram, the line connecting A and B has slope of -2 and the y-

Area of the triangle AOB = \(\frac{1}{2}\) OA * OB

Statement 1

(1) The x-coordinate of B is less than 7.

Area of the triangle when B = (7,0)

Equation of AB ⇒

\(y - y_1 = m (x - x_1) \)

\(y - 0 = -2 (x - 7) \)

y intercept ⇒ y = 14

Area of the triangle = 1/2 * 14 * 7 = 49 units^2

However, given that the x-coordinate of B is less than 7, the line AB can be any point towards the origin. The area of the triangle hence will be less than 49 sq. units. However, at some value of B, the area will be greater than 25 and for some value, the area will be less than 25.
The area of the triangle becomes smaller as we move line AB closer to the origin.


Hence the statement is not sufficient.

Statement 2

(2) The y-coordinate of A is greater than 11.

Area of the triangle when A = (0,11)

Equation of AB ⇒

\(y - y_1 = m (x - x_1) \)

\(y - 11 = -2 (x - 0) \)

x intercept ⇒ y = 11/2

Area of the triangle = 1/2 * 11/2 * 11 = 121/4 units^2 ⇒ i.e. greater than 30 sq.units

However, given that the x-coordinate of A is greater than 11, the line AB will be above the line when y coordinate is 11. Hence the area of the triangle will always be greater than 30 sq. units.



Hence the statement is sufficient.

Option B