Final answer:
The image point of (-9,-5) after the transformation T -5,0 followed by D 2 is (-8, -10) after applying the translation and then the dilation.
Step-by-step explanation:
The question is asking about the result of applying a composite transformation to a point in a coordinate plane.
Specifically, the student wants to find the image point of (-9,-5) after applying transformation T -5,0 followed by D 2 .
The transformation T -5,0 represents a translation (a shift of all points) by -5 units on the x-axis and 0 units on the y-axis.
The transformation D 2 represents a dilation from the origin (a scaling of all points) by a factor of 2. To find the image point:
- Apply the translation T -5,0 to the point (-9,-5) to get (-9 - (-5), -5 - 0) = (-4,-5).
- Apply the dilation D 2 to the translated point (-4,-5) to get (-4 * 2, -5 * 2) = (-8, -10).
Therefore, the image point after the transformation T -5,0 followed by D 2 is (-8, -10).