Mathematics

Problem

Consider the triangle with vertices

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.

Intuitive explanation

The key is recognizing that collinearity of three points means they all lie on the same line, which happens when the slopes between any two pairs are equal. Here, you'll use the condition that points $A$ , $B$ , and $C$ are collinear to set up an equation in $k$ —this forces the three vertices to lie on a single line, which determines the value of $k$ that makes them not form a proper triangle.

Intuitive explanation

Browse the problem library