Question

What transformation rule would represent a shift of 3 units to the left and 4 units down?

a) (x, y) -> (x - 3, y - 4)
b) (x, y) -> (x - 4y - 3)
c) (x, y) -> (4x, 3y)
d) (x, y) -> (x + 3, y + 4)

Answer 1

The transformation rule that corresponds to a shift of 3 units to the left and 4 units down is (x, y) -> (x - 3, y - 4). This means for each point, you subtract 3 from the x-coordinate and 4 from the y-coordinate.

Step-by-step explanation:

When looking at the given options to understand what transformation rule would represent a shift of 3 units to the left and 4 units down, we should recall that moving to the left on the x-axis means subtracting from the x-coordinate, and moving down on the y-axis means subtracting from the y-coordinate.

The correct transformation rule that describes this movement is option a) (x, y) -> (x - 3, y - 4).

This indicates that for any point (x, y), to shift it 3 units to the left, you subtract 3 from the x-coordinate. Similarly, to shift it 4 units down, you subtract 4 from the y-coordinate. So, the new position of the point after the transformation would be (x - 3, y - 4).