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NDA 2020 Maths · Mathematics · Straight Lines · easy

A line passes through the point (2,3) and the point is the midpoint of the part of the line lying between the coordinate axes. The equation of the…

Single correct option

A line passes through the point (2,3)(2,3) and the point is the midpoint of the part of the line lying between the coordinate axes. The equation of the line is
  1. A. 2x+3y=132x+3y=13
  2. B. 3x+2y=133x+2y=13
  3. C. 3x+2y=123x+2y=12
  4. D. x+y=5x+y=5
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Answer: (C) 3x+2y=123x+2y=12

If the midpoint is (2,3)(2,3) the intercepts are a=4a=4 on the x-axis and b=6b=6 on the y-axis, because the midpoint of (a,0)(a,0) and (0,b)(0,b) is (a2,b2)\left(\dfrac a2,\dfrac b2\right). The line is x4+y6=1\dfrac x4+\dfrac y6=1, i.e. 3x+2y=123x+2y=12. The option 3x+2y=133x+2y=13 is not even satisfied by the midpoint condition, and x+y=5x+y=5 passes through (2,3)(2,3) but cuts equal intercepts 5,55,5 whose midpoint is (52,52)\left(\tfrac52,\tfrac52\right).
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Original question written in the NDA 2020 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