Final answer:
The points have undergone a reflection, as indicated by a change in sign for both the x and y coordinates, resulting in a mirror image over the origin.
Step-by-step explanation:
The transformation of the points (-13, -5) to (13, 5) is a reflection. The coordinates of the initial point are both negated in the final point. This change in sign for both the x and y coordinates indicates that the point has been reflected over the origin.
In terms of movement in the coordinate system, transforming from (-13, -5) to (13, 5) involves moving horizontally to the right side of the coordinate system and vertically upward in the coordinate system. This because the x-value has changed from negative to positive, and the y-value has done the same. However, it's important to remember that a reflection is not the same as a translation; a reflection involves flipping over a line, whereas a translation would involve moving or sliding without flipping.