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NDA 2018 Maths · Mathematics · Straight Lines · hard

Triangle with vertices (0,0), (6,0) and (0,9): 1. Its centroid is (2,3). 2. Its orthocentre is (3,4.5).

Single correct option

Consider the following statements about the triangle with vertices (0,0)(0,0), (6,0)(6,0) and (0,9)(0,9):
1. Its centroid is (2,3)(2,3).
2. Its orthocentre is (3,4.5)(3,4.5).
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

The centroid is (0+6+03,0+0+93)=(2,3)\left(\frac{0+6+0}{3},\frac{0+0+9}{3}\right)=(2,3): statement 1 is correct. The triangle is right-angled at the origin, so the orthocentre is the right-angle vertex (0,0)(0,0); the point (3,4.5)(3,4.5) is the circumcentre (midpoint of the hypotenuse). Hence only statement 1 is correct.
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Original question written in the NDA 2018 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