A square is enclosed by the lines:

  1. \(\mathbf{r}=\begin{pmatrix}0\\2\end{pmatrix} + a\begin{pmatrix}1\\1\end{pmatrix}\)
  1. \(\mathbf{r}=\begin{pmatrix}0\\6\end{pmatrix} + b\begin{pmatrix}-1\\1\end{pmatrix}\)
  1. \(\mathbf{r}=\begin{pmatrix}2\\1\end{pmatrix} + c\begin{pmatrix}2\\2\end{pmatrix}\)
  1. \(\mathbf{r}=\begin{pmatrix}1\\2\end{pmatrix} + d\begin{pmatrix}1\\-1\end{pmatrix}\)

Find the area of the square.

The four lines represented on a coordinate grid, showing the enclosed square
  • Which line is which?
  • What are the positions of the vertices of the square?
  • Could you have predicted that the enclosed square would lie entirely within the first quadrant?