To solve this problem, let's go through it step by step.
1. Initial Coordinates of Point A:
Point [tex]\( A \)[/tex] has coordinates [tex]\((-4, -5)\)[/tex].
2. Translation Information:
- We need to translate the point 4 units to the right. Moving right means we add 4 to the x-coordinate.
- We also need to translate the point 5 units down. Moving down means we subtract 5 from the y-coordinate.
3. Calculate New Coordinates:
- For the x-coordinate: [tex]\( -4 + 4 \)[/tex]
- For the y-coordinate: [tex]\( -5 - 5 \)[/tex]
Let's compute these:
- New x-coordinate: [tex]\(-4 + 4 = 0\)[/tex]
- New y-coordinate: [tex]\(-5 - 5 = -10\)[/tex]
4. New Coordinates of Point [tex]\( A^{\prime} \)[/tex]:
After the translation, the new coordinates [tex]\( A^{\prime} \)[/tex] are [tex]\((0, -10)\)[/tex].
Thus, the coordinates of [tex]\( A^{\prime} \)[/tex] are [tex]\((0, -10)\)[/tex], which corresponds to option D.
Answer: [tex]\( D. (0, -10) \)[/tex]
