What Does Vector Coordinates Mean?

You can write a vector on vector coordinate form like this: $(x, y)$ . The vector coordinates show how the vector moves in the xy-plane.

Theory

The vector $(x, y)$ 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:

$\begin{array}{l} (2, 5), (- 5, 1), (- 78, - 3), \\ (0, - 6), (- 48, 0), (0, 0) . \end{array}$

$(2, 5), (- 5, 1), (- 78, - 3), (0, - 6), (- 48, 0), (0, 0) .$

The vector (2, 5)

$(2, 5)$ moves $2$ steps in the positive $x$ -direction and $5$ steps in the positive $y$ -direction.

The vector (-5, 1)

$(- 5, 1)$ moves $5$ steps in the negative $x$ -direction and $1$ step in the positive $y$ -direction.

The vector (-78, -3)

$(- 78, - 3)$ moves $78$ steps in the negative $x$ -direction and $3$ steps in the negative $y$ -direction.

The vector (0, -6)

$(0, - 6)$ doesn’t move in the $x$ -direction at all, but moves $6$ steps in the negative $y$ -direction.

The vector (-48, 0)

$(- 48, 0)$ moves $48$ steps in the negative $x$ -direction, but doesn’t move in the $y$ -direction.

$(0, 0)$ moves neither in the $x$ -direction nor the $y$ -direction.

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