Let's go through the process of translating each ordered pair by the given translation vector [tex]\( T(0, 5) \)[/tex]. The translation vector means we are adding 0 to the x-coordinate and 5 to the y-coordinate of each point.
### Step-by-Step Solution:
1. Translate (9, 0):
- Original pair: (9, 0)
- Apply the translation vector [tex]\( T(0, 5) \)[/tex]:
- New x-coordinate [tex]\( = 9 + 0 = 9 \)[/tex]
- New y-coordinate [tex]\( = 0 + 5 = 5 \)[/tex]
- Therefore, the translated pair is (9, 5).
2. Translate (2, -4):
- Original pair: (2, -4)
- Apply the translation vector [tex]\( T(0, 5) \)[/tex]:
- New x-coordinate [tex]\( = 2 + 0 = 2 \)[/tex]
- New y-coordinate [tex]\( = -4 + 5 = 1 \)[/tex]
- Therefore, the translated pair is (2, 1).
So, the translated ordered pairs are:
- (9, 5)
- (2, 1)
Comparing these results with the options provided, the correct pairs after applying the translation are:
[tex]\[
(9, 5) \text{ and } (2, 1)
\][/tex]
The other pairs listed in the options do not match the correct translated pairs. Hence, the correct answer is:
[tex]\[
(9, 5) \text{ and } (2, 1)
\][/tex]
