Comprehension

Direction: Consider the following for the items that follow:

ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2, 3), B(4, 3), C(5, 1) be the vertices.

What are the coordinates of vertex D?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. (2, 1)
  2. (1, 2)
  3. (1, 1)
  4. (3, 1)

Answer (Detailed Solution Below)

Option 4 : (3, 1)
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Detailed Solution

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Explanation:

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In isosceles trapezium, diagonals bisect each other.

O is the midpoint of AC and BD

Then, \(\frac{5+2}{2} = \frac{4+a}{2}, \frac{3+b}{2} = \frac{3+1}{2}\)

⇒ a = 3, b = 1 

⇒ D(a, b) = (3, 1)

∴ Option (d) is correct

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