What happens to the coordinates of a point after a translation of (x, y) by (a, b)?

When a point with coordinates (x, y) undergoes a translation by the vector (a, b), the new position of the point is determined by adding the components of the vector to the original coordinates. Specifically, the x-coordinate increases by a (the horizontal component of the translation), and the y-coordinate increases by b (the vertical component of the translation). This is why the resulting coordinates after the translation become (x + a, y + b).

This transformation effectively shifts the point in space by a certain amount defined by the vector, allowing it to move to a new location without altering its orientation or size. The choice that indicates this result accurately captures the action of a translation.