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The triangle with vertices (k, 0), (4, 0) and (0, 2) has area 8 square units. Find both values of k.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The triangle with vertices $(k, 0)$ , $(4, 0)$ and $(0, 2)$ has area $8$ square units. Find both values of $k$ .

\displaystyle \begin{vmatrix} k & 0 & 1 \\ 4 & 0 & 1 \\ 0 & 2 & 1 \end{vmatrix}

$. Expand along the middle column.

Need a reminder? The key ideaShow

The area of the triangle with vertices $(x_i, y_i)$ is $\tfrac{1}{2}\left|\det\right|$ of the matrix with rows $(x_i, y_i, 1)$ . Three points are collinear exactly when this determinant is $0$ . A matrix multiplies every area by $|\det T|$ .

The worked solution

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