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COMEDK2022MathematicsStraight Lines

The slope of lines which makes an angle 45^ with the line 2 x-y=-7

Options

  1. A1 3 ,-3
  2. B-1,1
  3. C3, -1 3
  4. D1, 1 3

Correct answer

A. 1 3 ,-3

Step-by-step solution

The given line is 2x - y = -7 , which can be written as y = 2x + 7 . The slope of this line is m₁ = 2 . Let the slope of the required line be m . The angle between the two lines is 45^ . Using the formula for the angle between two lines, = | m - m₁ 1 + m m₁ | , we have: 45^ = | m - 2 1 + 2m | 1 = | m - 2 1 + 2m | This gives two cases: Case 1: m - 2 1 + 2m = 1 m - 2 = 1 + 2m m = -3 . Case 2: m - 2 1 + 2m = -1 m - 2 = -1 - 2m 3m = 1 m = 1 3 . Thus, the slopes are -3 and 1 3 . Answer: 1 3 ,-3

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