To find the coordinates of the vertices after the translation, you need to apply the given translation vector to each vertex of the original triangle.
Given the translation "right 2 units and 3 units down," you need to add 2 to the x-coordinate and subtract 3 from the y-coordinate of each vertex.
Let's evaluate each answer choice using this translation:
a. S'(-9, 12), T'(-12, 5), U'(-6, 5):
- This choice does not align with the given translation. It shows a translation up instead of down.
b. S'(-4, 7), T'(-7, 0), U'(-1, 0):
- This choice aligns with the given translation. Let's verify it with the translation rules.
- Applying the translation vector (2, -3) to each vertex:
- For S: (-4 + 2, 7 - 3) = (-2, 4)
- For T: (-7 + 2, 0 - 3) = (-5, -3)
- For U: (-1 + 2, 0 - 3) = (1, -3)
- Hence, this choice is most likely the correct answer.
c. S'(-8, 13), T'(-11, 6), U'(-5, 6):
- This choice does not align with the given translation. It shows a translation up instead of down.
d. S'(-4, 10), T'(-7, 3), U'(-1, 3):
- This choice does not align with the given translation. It shows a translation up instead of down.
Based on the above analysis, the correct answer is b. S'(-4, 7), T'(-7, 0), U'(-1, 0).