Final answer:
The image point of (-4,9) after the transformation T0,3 followed by D5 is (-20,60), which is first translated by (0,3) and then dilated by a factor of 5.
Step-by-step explanation:
The initial point given is (-4,9). The transformation T0,3 o D5 implies a translation by (0,3) followed by a dilation by a factor of 5. Translation moves each point in a figure the same distance in the same direction. Dilation multiplies the coordinates of each point by the same factor.
First, we translate the point (-4,9) by (0,3):
- (-4 + 0, 9 + 3) = (-4, 12)
After translation, the point is at (-4,12).
Next, we apply dilation by a factor of 5:
- (-4 × 5, 12 × 5) = (-20, 60)
After dilation, the image point is at (-20,60).