Straight Line Question 4

Question: If the coordinates of the vertices A, B, C of the triangle ABC be $ (-\ 4,\ 2), $ $ (12,\ -2) $ and $ (8,\ 6) $ respectively, then $ \angle \ B $ =

Options:

A) $ {{\tan }^{-1}}( -\frac{6}{7} ) $

B) $ {{\tan }^{-1}}( \frac{6}{7} ) $

C) $ {{\tan }^{-1}}( -\frac{7}{6} ) $

D) $ {{\tan }^{-1}}( \frac{7}{6} ) $

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Answer:

Correct Answer: D

Solution:

  • Here equation of AB is $ x+4y-4=0 $ …..(i) and equation of BC is $ 2x+y-22=0 $ …..(ii) Thus angle between (i) and (ii) is given by $ {{\tan }^{-1}}\frac{-\frac{1}{4}+2}{1+( -\frac{1}{4} )(-2)}={{\tan }^{-1}}\frac{7}{6} $ .