To translate the point U(-6, 3) by the rule (x, y) → (x - 7, y + 4), you subtract 7 from the x-coordinate and add 4 to the y-coordinate, resulting in the image point U'(-13, 7).
The student is asking how to perform a translation of a point on the coordinate plane. In this case, the initial point is U(-6, 3), and the translation to be applied is (x - 7, y + 4). The translation statement involves adding the first number in the ordered pair to the x-coordinate of the point and the second number to the y-coordinate of the point.
To translate U(-6, 3) by (x, y) → (x - 7, y + 4), you do the following:
Take the x-coordinate of U, which is -6, and subtract 7: -6 - 7 = -13.
Take the y-coordinate of U, which is 3, and add 4: 3 + 4 = 7.
The image of point U after translation is U'(-13, 7).