Answer:
(1, 2)
Explanation:
Remember that the final shape and position of a figure after a transformation is called the image, and the original shape and position of the figure is the pre-image.
In our case, our figure is just a point. We know that after the transformation T : (x, y) → (x + 3, y + 1), our image has coordinates (4, 3).
The transformation rule T : (x, y) → (x + 3, y + 1) means that we add 3 to the x-coordinate and add 1 to the y-coordinate of our pre-image. Now to find the pre-image of our point, we just need to reverse those operations; in other words, we will subtract 3 from the x-coordinate and subtract 1 from the y-coordinate.
So, our rule to find the pre-image of the point (4, 3) is:
T : (x, y) → (x - 3, y - 1)
We know that the x-coordinate of our image is 4 and its y-coordinate is 3.
Replacing values:
(4 - 3, 3 - 1)
(1, 2)
We can conclude that our pre-image is the point (1, 2).