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Question:

Direction: Each of these items has a question followed by two statements, I and II. Mark the answer

1. if the question can be answered with the help of one statement alone.
2. if the question can be answered with the help of any one statement independently.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.

What is the area bounded by the two lines and the coordinate axes in the first quadrant?

I. The lines intersect at a point which also lies on the lines 3x – 4y = 1 and 7x – 8y = 5.
II. The lines are perpendicular, and one of them intersects the Y-axis at an intercept of 4.

Explanation:

If we solve the two given equations, we get the point of intersection as (3, 2). Let A = (3, 2). The lines of our interest (let it be L₁ and L₂) also pass through A. One of the lines passes through (0, 4). Let L₁ passes through (0, 4), but it also passes through (3, 2). Hence, we can find the slope of L₂ (which is equal to – $\frac{2}{3}$ ). Hence, slope of L₂ will be $\frac{3}{2}$ since L₁ and L₂ are perpendicular.
Hence, equations of L₁ and L₂ can be obtained by using slope point form. (Students! we need not really find out the equations.) After getting both the equations, we can find the area bounded by L₁ and L₂and coordinate axes.

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