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

Example 2 - Chapter 10 Class 11 Straight Lines - Part 2
Example 2 - Chapter 10 Class 11 Straight Lines - Part 3

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Example 2 If the angle between two lines is π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 ΞΈ = |(π‘š2 βˆ’ π‘š1)/(1 + π‘š1π‘š2)| Putting ΞΈ = πœ‹/4 = 180/4 = 45Β° 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 ΞΈ = |(π‘š2 βˆ’ π‘š1)/(1 + π‘š1π‘š2)| tan 45Β° = |(π‘š2 βˆ’ 1/2)/(1 + 1/2 π‘š2)| 1 = |((2π‘š_2 βˆ’ 1)/2)/((2 + π‘š_2)/2)| 1 = |(2π‘š2 βˆ’ 1)/(2 + π‘š2)| |(2π‘š2 βˆ’ 1)/(2 + π‘š2)|= 1 So, (2π‘š2 βˆ’ 1)/(2 + π‘š2) = 1 & (2π‘š2 βˆ’ 1)/(2 + π‘š2) = –1 Therefore m2 = 3 or m2 = (βˆ’1)/3 . Hence, Slope of the other line is 3 or (βˆ’πŸ)/πŸ‘ (πŸπ’ŽπŸ βˆ’ 𝟏)/(𝟐 + π’ŽπŸ) = 1 2m2 – 1 = (2 + m2) 2m2 – m2 = 2 + 1 m2 = 3 (πŸπ’ŽπŸ βˆ’ 𝟏)/(𝟐 + π’ŽπŸ) = –1 2m2 – 1 = –(2 + m2) 2m2 – 1 = –2 – m2 2m2 + m2 = –2 + 1 3m2 = –1 m2 = (βˆ’1)/3

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.