# Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units.

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Let k be an integer such that the 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 :

(1) 2, -1/2
(2) 1, 3/4
(3) 1, -3/4
(4) 2, 1/2

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Solution:

k = 2

Orthocentre is 2, 1/2

The correct option is (4).