Final answer:
The transformed figure will be three times larger than the original figure and positioned 6 units lower on the y-axis after a dilation by a scale factor of 3 and a translation 6 units down.
Step-by-step explanation:
When a figure on the coordinate plane is dilated by a scale factor of 3, each point of the original figure moves away from the origin (0,0) by three times its original distance. This means that if a point on the original figure is at a certain distance from the origin, after the dilation, it will be at three times that distance from the origin. Consequently, the transformed figure will be three times larger than the original figure - it's an enlargement.
After dilation, when the figure is translated 6 units down, each point of the dilated figure is moved 6 units down along the y-axis. This translation does not affect the size or shape of the figure, only its position on the coordinate plane. As a result, the transformed figure will maintain its enlarged size but will be located 6 units lower than the dilated position.
In summary, the transformed figure will be proportionally identical to the original figure but will be larger by a factor of 3 and positioned 6 units lower on the coordinate plane.