Let k be an integer such that triangle with vertices k 3k 5 k and k 2 has area 28 sq units Then the orthocentre of this triangle is at the point JEE MAINS Mathematics 2017

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## Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :-JEE MAINS-Mathematics-2017

(1)(2,1/2)

(2)(2,-1/2)

(3)(1,3/4)

(4)(1,-3/4)

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Austin-Hunter

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We have(3X3 matrix)
| k 3k 1 |
(1/2) | 5  k 1 |= 28
| k 2  1 |
5k2 + 13k – 46 = 0
or
5k2 + 13k + 66 = 0 (no real solution exist)
k =–23/5 or k = 2
As k is an integer, so k=2
orthocentre is (2,1/2)

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