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NDA 2019 Maths · Mathematics · Straight Lines · easy

The lines x+y=4 and 2x-y=2 meet at a point P. The line through P perpendicular to x+2y=3 is

Single correct option

The lines x+y=4x+y=4 and 2x−y=22x-y=2 meet at a point PP. The line through PP perpendicular to x+2y=3x+2y=3 is
  1. A. x+2y−6=0x+2y-6=0
  2. B. 2x+y−6=02x+y-6=0
  3. C. 2x−y−2=02x-y-2=0
  4. D. x−2y+2=0x-2y+2=0
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Answer: (C) 2x−y−2=02x-y-2=0

Solving x+y=4x+y=4, 2x−y=22x-y=2 gives P=(2,2)P=(2,2). The line x+2y=3x+2y=3 has slope −12-\frac12, so a perpendicular line has slope 22. Through (2,2)(2,2): y−2=2(x−2)y-2=2(x-2), i.e. 2x−y−2=02x-y-2=0. The option x+2y−6=0x+2y-6=0 is the line through PP parallel to the given line, a typical trap.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake