Straight Line Question 36

Question: If vertices of a parallelogram are respectively (0, 0), (1, 0), (2, 2) and (1, 2), then angle between diagonals is [RPET 1996]

Options:

A) $ \pi /3 $

B) $ \pi /2 $

C) $ 3\pi /2 $

D) $ \pi /4 $

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Answer:

Correct Answer: D

Solution:

  • Here, Slope of Ist diagonal= $ m_1=\frac{2-0}{2-0}=1\Rightarrow {\theta_1}=45^{o} $ Slope of IInd diagonal= $ m_2=\frac{2-0}{1-1}=\infty \Rightarrow {\theta_2}=90^{o} $
    Þ $ {\theta_2}-{\theta_1}=45^{o}=\frac{\pi }{4} $ .