Let be an integer such that the triangle with vertices

MATHEMATICS · Single correct · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

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)

\left(2, \frac{1}{2}\right)

(2)

\left(2, -\frac{1}{2}\right)

(3)

\left(1, \frac{3}{4}\right)

(4)

\left(1, -\frac{3}{4}\right)