Multiple choice

If centroid and circumcentre of a triangle are (-2, 3) and (4, 1) respectively, then its orthocentre is

  1. (7, -14)

  2. (-7, -14)

  3. (-14, 7)

  4. (-14, -7)
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C Correct answer
Explanation

The centroid G divides the line segment joining the orthocentre H and circumcentre O in the ratio 2:1. Let H = (x, y). G = (2O + H) / 3. (-2, 3) = (2(4, 1) + (x, y)) / 3. -6 = 8 + x => x = -14. 9 = 2 + y => y = 7. H = (-14, 7).

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