What is the image of a point (4, 5) after translation by the vector (-1, 3)?

The image of the point (4, 5) after translation by the vector (-1, 3) is (3, 8).

In more detail, translation is a type of transformation that slides each point of a shape or object a certain distance in a specified direction. When translating a point, you add the components of the translation vector to the coordinates of the original point.

For the point (4, 5), we are given the translation vector (-1, 3). This vector tells us to move the point 1 unit to the left (because of the -1) and 3 units up (because of the 3).

To find the new coordinates, you simply add the x-component of the vector to the x-coordinate of the point, and the y-component of the vector to the y-coordinate of the point. So, for the x-coordinate: 4 + (-1) = 3. For the y-coordinate: 5 + 3 = 8.

Therefore, after applying the translation vector (-1, 3) to the point (4, 5), the new coordinates are (3, 8). This means the point has moved to the left by 1 unit and up by 3 units, resulting in its new position at (3, 8).