# What Does Vector Coordinates Mean?

You can write a vector on vector coordinate form like this: $\phantom{\rule{-0.17em}{0ex}}\left(x,y\right)$. The vector coordinates show how the vector moves in the xy-plane.

Theory

### Vectorcoordinate

The vector $\phantom{\rule{-0.17em}{0ex}}\left(x,y\right)$ tells you that it moves $x$ steps along the $x$-axis and $y$ steps along the $y$-axis.

Example 1

Explain how these vectors move:

$\begin{array}{llll}\hfill & \phantom{\rule{-0.17em}{0ex}}\left(2,5\right),\phantom{\rule{-0.17em}{0ex}}\left(-5,1\right),\phantom{\rule{-0.17em}{0ex}}\left(-78,-3\right),\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{-0.17em}{0ex}}\left(0,-6\right),\phantom{\rule{-0.17em}{0ex}}\left(-48,0\right),\phantom{\rule{-0.17em}{0ex}}\left(0,0\right).\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $\phantom{\rule{-0.17em}{0ex}}\left(2,5\right),\phantom{\rule{-0.17em}{0ex}}\left(-5,1\right),\phantom{\rule{-0.17em}{0ex}}\left(-78,-3\right),\phantom{\rule{-0.17em}{0ex}}\left(0,-6\right),\phantom{\rule{-0.17em}{0ex}}\left(-48,0\right),\phantom{\rule{-0.17em}{0ex}}\left(0,0\right).$

$\phantom{\rule{-0.17em}{0ex}}\left(2,5\right)$ moves $2$ steps in the positive $x$-direction and $5$ steps in the positive $y$-direction.

$\phantom{\rule{-0.17em}{0ex}}\left(-5,1\right)$ moves $5$ steps in the negative $x$-direction and $1$ step in the positive $y$-direction.

$\phantom{\rule{-0.17em}{0ex}}\left(-78,-3\right)$ moves $78$ steps in the negative $x$-direction and $3$ steps in the negative $y$-direction.

$\phantom{\rule{-0.17em}{0ex}}\left(0,-6\right)$ doesn’t move in the $x$-direction at all, but moves $6$ steps in the negative $y$-direction.

$\phantom{\rule{-0.17em}{0ex}}\left(-48,0\right)$ moves $48$ steps in the negative $x$-direction, but doesn’t move in the $y$-direction.

1

$\phantom{\rule{-0.17em}{0ex}}\left(0,0\right)$ moves neither in the $x$-direction nor the $y$-direction.