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Mathematics-2017-->View question

By:Purnima

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leo

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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)

By:Purnima

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## Answers

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)

leo

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