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Examples

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Last updated at Sept. 6, 2021 by Teachoo

Example 2 If the angle between two lines is π/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 = |(π2 β π1)/(1 + π1π2)| Putting ΞΈ = π/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 = |(π2 β π1)/(1 + π1π2)| tan 45Β° = |(π2 β 1/2)/(1 + 1/2 π2)| 1 = |((2π_2 β 1)/2)/((2 + π_2)/2)| 1 = |(2π2 β 1)/(2 + π2)| |(2π2 β 1)/(2 + π2)|= 1 So, (2π2 β 1)/(2 + π2) = 1 & (2π2 β 1)/(2 + π2) = β1 Therefore m2 = 3 or m2 = (β1)/3 . Hence, Slope of the other line is 3 or (βπ)/π (πππ β π)/(π + ππ) = 1 2m2 β 1 = (2 + m2) 2m2 β m2 = 2 + 1 m2 = 3 (πππ β π)/(π + ππ) = β1 2m2 β 1 = β(2 + m2) 2m2 β 1 = β2 β m2 2m2 + m2 = β2 + 1 3m2 = β1 m2 = (β1)/3