Comprehension

These questions are based on the situation given below:
A rectangle PRSU is divided into two smaller rectangles PQTU and QRST by the line TQ. \( PQ = 10 \, \text{cm}, \quad QR = 5 \, \text{cm}, \quad RS = 10 \, \text{cm} \). Points A, B, F are within the rectangle PQTU and, points C, D, E are within the rectangle QRST. The closest pair of points among the pairs \( (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) \) are \( \frac{10}{\sqrt{3}} \, \text{cm} \) apart.

Question: 1

Which of the following statements is necessarily true?

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In problems involving distances between points, always calculate the distance between each pair and compare them to determine the closest points.
Updated On: Aug 5, 2025
  • The closest pair of points among the six given points cannot be (F, C).
  • Distance between A and B is greater than distance between F and C.
  • The closest pair of points among 6 given points (C,D), (D,E) or (C,E).
  • None of the above.
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The Correct Option is A

Solution and Explanation

Given the coordinates of the points and the distances between them, the closest pair of points is never (F, C), as the distance between them is not the smallest compared to other pairs. Based on the geometry of the rectangle, the answer is option (1).
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Question: 2

AB \(>\) AF; CD \(>\) DE \(>\) CE, BF = \( 6\sqrt{5} \) cm. Which is the closest pair of points among all 6 given points?

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When working with geometric problems involving distances, use the distance formula to compute and compare distances between all points.
Updated On: Aug 5, 2025
  • B, F
  • C, D
  • A, B
  • None of these
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The Correct Option is B

Solution and Explanation

After calculating the distances between all pairs of points, the closest pair of points is (C, D), as the distance is smaller compared to other pairs. Hence, option (2) is correct.
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