What is the vector translation from point (0, 0) to point (6, -3)?

The vector translation from point (0, 0) to point (6, -3) is (6, -3).

In more detail, a vector translation describes how a point moves from one location to another in a coordinate system. The vector itself is written as an ordered pair (x, y), where 'x' represents the horizontal movement and 'y' represents the vertical movement. In this case, we start at the origin, which is the point (0, 0). To reach the point (6, -3), we move 6 units to the right (positive direction on the x-axis) and 3 units down (negative direction on the y-axis).

To find the vector translation, you subtract the coordinates of the starting point from the coordinates of the ending point. So, for the x-coordinate: 6 - 0 = 6, and for the y-coordinate: -3 - 0 = -3. Therefore, the vector translation is (6, -3).

This means that if you were to draw an arrow from the origin (0, 0) to the point (6, -3), the arrow would move 6 units to the right and 3 units down. This vector tells you exactly how far and in which direction you need to move to get from the starting point to the ending point. Understanding vector translations is useful in many areas of mathematics and physics, as it helps describe movement and position changes in a clear and concise way.