Consider the triangle with vertices

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

A(2k, k)

B(k+3, 2k-1)

and

C(1, -4)

. (a) Show that the area of triangle ABC simplifies to

\tfrac{1}{2}\lvert 3k^2 - 2k - 11 \rvert

square units. (b) Hence determine all integer values of

k

for which the area of the triangle is

18

square units.