A rectangle is bound by the lines 𝑥 = 0;𝑦 = 0;𝑥 = 5 and 𝑦 = 3. The line…
2019
A rectangle is bound by the lines 𝑥 = 0;𝑦 = 0;𝑥 = 5 and 𝑦 = 3. The line segment joining (−1,0) and (4,5), if clipped against this window will connect the points __________.
- A.
(0,1) and (3,3)
- B.
(0,1) and (2,3)
- C.
(0,1) and (4,5)
- D.
(0,1) and (3, 5)
Attempted by 68 students.
Show answer & explanation
Correct answer: B
Solution: Find the intersections of the line segment with the rectangle boundaries.
Step 1: Parameterize the segment from (-1,0) to (4,5).
Parameterization: P(t) = (-1 + 5t, 0 + 5t), for t in [0,1].
Intersect with x = 0: solve -1 + 5t = 0 → t = 0.2, giving point (0,1).
Intersect with y = 3: solve 5t = 3 → t = 0.6, giving point (2,3).
Step 2: Verify both intersections lie on the segment: t = 0.2 and t = 0.6 are within [0,1], so both points are valid clipped endpoints inside the rectangle.
Conclusion: The clipped segment connects (0,1) and (2,3).