Last updated at Feb. 3, 2020 by Teachoo
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Example 2 If the angle between two lines is ๐/4 and slope of one of the lines is 1/2, find the slope of the other line. We know that angle between two lines are tan ฮธ = |(๐2 โ ๐1)/(1 + ๐1๐2)| Putting ฮธ = ๐/4 = 180/4 = 45ยฐ Let m1 and m2 be the slope of 2 lines So, m1 = 1/2 We need to find slope of 2nd line i.e. m2 Putting values in formula tan ฮธ = |(๐2 โ ๐1)/(1 + ๐1๐2)| tan 45ยฐ = |(๐2 โ 1/2)/(1 + 1/2 ๐2)| 1 = |((2๐_2 โ 1)/2)/((2 + ๐_2)/2)| 1 = |(2๐2 โ 1)/(2 + ๐2)| |(2๐2 โ 1)/(2 + ๐2)|= 1 So, (2๐2 โ 1)/(2 + ๐2) = 1 & (2๐2 โ 1)/(2 + ๐2) = โ1 Therefore m2 = 3 or m2 = (โ1)/3 . Hence, Slope of the other line is 3 or (โ๐)/๐ (๐๐๐ โ ๐)/(๐ + ๐๐) = 1 2m2 โ 1 = (2 + m2) 2m2 โ m2 = 2 + 1 m2 = 3 (๐๐๐ โ ๐)/(๐ + ๐๐) = โ1 2m2 โ 1 = โ(2 + m2) 2m2 โ 1 = โ2 โ m2 2m2 + m2 = โ2 + 1 3m2 = โ1 m2 = (โ1)/3
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