What is the final position of a point at (4, 2) after a translation of (-2, 3)?

To determine the final position of a point after a translation, you need to apply the translation vector to the original point's coordinates. In this case, you start with the point at (4, 2) and are translating it by the vector (-2, 3).

The translation affects the x-coordinate and the y-coordinate separately. For the x-coordinate, you subtract 2 from the original x-coordinate:

4 (original x-coordinate) + (-2) (change in x) = 4 - 2 = 2.

Next, for the y-coordinate, you add 3 to the original y-coordinate:

2 (original y-coordinate) + 3 (change in y) = 2 + 3 = 5.

Combining both results gives you the new position of the point after the translation, which is (2, 5).

This calculation shows that the correct final position of the point after the specified translation is indeed (2, 5).