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

  1. Chapter 10 Class 11 Straight Lines (Term 1)
  2. Serial order wise

Transcript

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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.