Quantitative Aptitude Ques 2191

Question: The vertices of a quadrilateral ABCD are A (0, 0), B (4, 4), C (4, 8) and D (0, 4). Then, ABCD is a

Options:

A) square

B) rhombus

C) rectangle

D) parallelogram

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ AB^{2}={{(4-0)}^{2}}+{{(4-0)}^{2}}=32 $ $ BC^{2}={{(4-4)}^{2}}+{{(8-4)}^{2}} $ $ =0+16=16 $ $ CD^{2}={{(0-4)}^{2}}+{{(4-8)}^{2}} $ $ =16+16=32 $ $ AD^{2}={{(0-0)}^{2}}+{{(4-0)}^{2}} $ $ =(0+16)=16 $ $ AB=CD=\sqrt{32}=4\sqrt{2} $ $ BC=AD=\sqrt{16}=4 $ $ AC^{2}={{(4-0)}^{2}}+{{(8-0)}^{2}}=16+64=80 $ $ BD^{2}={{(0-4)}^{2}}+{{(4-4)}^{2}}=16+0=16 $

$ \therefore $ Diagonal AC $ \ne $ Diagonal BD So, ABCD is a parallelogram.

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