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Example 2 - If angle between two lines is pi/4, slope is 1/2 - Examples

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Example 2 If the angle between two lines is ๐œ‹/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 = |(๐‘š2 โˆ’ ๐‘š1)/(1 + ๐‘š1๐‘š2)| Putting ฮธ = ๐œ‹/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 = |(๐‘š2 โˆ’ ๐‘š1)/(1 + ๐‘š1๐‘š2)| tan 45ยฐ = |(๐‘š2 โˆ’ 1/2)/(1 + 1/2 ๐‘š2)| 1 = |((2๐‘š_2 โˆ’ 1)/2)/((2 +๐‘š_2)/2)| 1 = |(2๐‘š2 โˆ’ 1)/(2 + ๐‘š2)| |(2๐‘š2 โˆ’ 1)/(2 + ๐‘š2)|= 1 So, (2๐‘š2 โˆ’ 1)/(2 + ๐‘š2) = 1 & (2๐‘š2 โˆ’ 1)/(2 + ๐‘š2) = โ€“ 1 Therefore m2 = 3 or m2 = (โˆ’1)/3 . Hence, Slope of the other line is 3 or (โˆ’1)/3

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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