Question

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 $3x - 4y = 1$ and $7x - 8y = 5$.
II. The lines are perpendicular, and one of them intersects the Y-axis at an intercept of 4.

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

Intersection and slope/intercept information together can fully determine line equations.

Answer 1

The Correct Option is C

I alone: Gives intersection point but not intercepts with axes. Insufficient.
II alone: Gives perpendicular slope relation and one intercept, but missing the other intercept. Insufficient.
Together: We can find both lines’ equations, intercepts, and thus area.