Translating Shapes

The negative value $(-4)$ tells us to move 4 units left, and the positive value $(2)$ tells us to move 2 units up.

The negative value $(-3)$ tells us to move 3 units left, and the negative value $(-6)$ tells us to move 6 units down.

The positive 7 on the top means moving 7 units to the right, and the -3 at the bottom means moving 3 units down.

To read a column vector from a diagram, start at the beginning of the arrow. First count the horizontal movement. It is 5 units to the left, so the top number is -5. Then count the vertical movement. It is 2 units down, so the bottom number is -2. That gives the vector $\left(\begin{array}{c}-5\\ -2\end{array}\right)$.

To find the new coordinates, subtract 3 from the $x$-coordinate: $2-3=-1$ and subtract 4 from the $y$-coordinate: $5-4=1$, which gives $(-1,1)$.

To find the column vector, count the horizontal movement (5 units left) and the vertical movement (3 units up). This gives the vector $\left(\begin{array}{c}-5\\ 3\end{array}\right)$.