To find the coordinates of [tex]\( H' \)[/tex] after the translation, we can follow these steps:
1. Identify the original coordinates of point [tex]\( H \)[/tex] (pre-image):
The coordinates of [tex]\( H \)[/tex] are [tex]\( (-2, 3) \)[/tex].
2. Identify the translation rule:
The translation rule given is [tex]\( T_{-5, 9} \)[/tex]([tex]\(x, y\)[/tex]). This means that for any point [tex]\( (x, y) \)[/tex], the new coordinates [tex]\( (x', y') \)[/tex] after translation will be:
[tex]\[
x' = x + (-5)
\][/tex]
[tex]\[
y' = y + 9
\][/tex]
3. Apply the translation rule to the coordinates of [tex]\( H \)[/tex]:
- For the x-coordinate:
[tex]\[
x' = -2 + (-5) = -2 - 5 = -7
\][/tex]
- For the y-coordinate:
[tex]\[
y' = 3 + 9 = 12
\][/tex]
4. Combine the new coordinates:
Therefore, the coordinates of [tex]\( H' \)[/tex] after the translation are:
[tex]\[
(-7, 12)
\][/tex]
Given the multiple choices:
- [tex]\( (7, -8) \)[/tex]
- [tex]\( (-7, 6) \)[/tex]
- [tex]\( (3, -12) \)[/tex]
- [tex]\( (2, 1) \)[/tex]
The coordinates [tex]\( (-7, 12) \)[/tex] match none of these options exactly. Therefore, it seems there might be a mistake in the options provided. The correct translated coordinates for [tex]\( H' \)[/tex] are [tex]\( (-7, 12) \)[/tex].
