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NDA 2024 Maths · Mathematics · Straight Lines · medium

The perpendicular distance of the origin from the line joining the points (6,0) and (0,8) is

Single correct option

The perpendicular distance of the origin from the line joining the points (6,0)(6,0) and (0,8)(0,8) is
  1. A. 524\frac{5}{24}
  2. B. 245\frac{24}{5}
  3. C. 1010
  4. D. 77
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Answer: (B) 245\frac{24}{5}

The line in intercept form is x6+y8=1\frac x6+\frac y8=1, i.e. 4x+3y−24=04x+3y-24=0. The distance from the origin is 2416+9=245\frac{24}{\sqrt{16+9}}=\frac{24}{5}. Cross-check by areas: the triangle with legs 6 and 8 has hypotenuse 10, and altitude =6⋅810=4.8=\frac{6\cdot8}{10}=4.8. Trap: 10 is the hypotenuse, and 524\frac5{24} inverts the answer.
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Original question written in the NDA 2024 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